Muzibur Rahman Mozumder

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On Semiprime Rings with Generalized Derivations

2010-08-13

Nadeem ur Rehman , Mohammad Ashraf , Shakir Ali +1 more

Let R be a ring and F and G be generalized derivations ofR with associated derivations d and g respectively. In the present paper,we shall investigate the commutativity of semiprime … Let R be a ring and F and G be generalized derivations ofR with associated derivations d and g respectively. In the present paper,we shall investigate the commutativity of semiprime ring R admitting generalizedderivations F and G satisfying any one of the properties: (i)F(x)x =xG(x); (ii) [F(x); d(y)] = [x; y]; (iii) F([x; y]) = [d(x); F(y)]; (iv) d(x)F(y) =xy; (v) F(x2) = x2; (vi) [F(x); y] = [x;G(y)]; (vii) F([x; y]) = [F(x); y]+[d(y); x] and(viii) F(x ◦ y) = F(x) ◦ y − d(y) ◦ x for all x; y in some appropriate subset of R.

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ON GENERALIZED (σ, τ)-BIDERIVATIONS IN RINGS

2011-09-01

Mohammad Ashraf , Nadeem ur Rehman , Shakir Ali +1 more

Let σ, τ be automorphisms of a ring R. In the present paper many concepts related to biadditive mappings of rings, viz. σ-left centralizer traces, symmetric generalized (σ, τ)-biderivations, σ-left … Let σ, τ be automorphisms of a ring R. In the present paper many concepts related to biadditive mappings of rings, viz. σ-left centralizer traces, symmetric generalized (σ, τ)-biderivations, σ-left bimultipliers and symmetric generalized Jordan (σ, τ)-biderivations are studied. Many results related to these concepts are given. It is established that every symmetric generalized (σ, τ)-biderivation of a prime ring of characteristic different from 2, can be reduced to a σ-left bimultiplier under certain algebraic conditions. Further, it is shown that every symmetric generalized Jordan (σ, τ)-biderivation of a prime ring of characteristic different from 2 is a symmetric generalized (σ, τ)-biderivation.

MAPS ACTING ON SOME ZERO PRODUCTS

2014-01-01

Hung‐Yuan Chen , Kun-Shan Liu , Muzibur Rahman Mozumder

Let $R$ be a prime ring with nontrivial idempotents. Assume $\ast$ is an involution of $R$. In this note we characterize the additive map $\delta \colon R \to R$ such … Let $R$ be a prime ring with nontrivial idempotents. Assume $\ast$ is an involution of $R$. In this note we characterize the additive map $\delta \colon R \to R$ such that $\delta(x) y^\ast + x \delta(y)^\ast = 0$ whenever $xy^\ast = 0$ and $\phi \colon R \to R$ such that $\phi(x) \phi(y)^\ast = 0$ whenever $xy^\ast = 0$.

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A note on skew Lie product of prime ring with involution

2020-01-01

Adnan Abbasi , Muzibur Rahman Mozumder , Nadeem Ahmad Dar

Let R be a ring with involution.The skew Lie product of a, b ∈ R is defined by [a, b] = abba * .In the present paper we study prime … Let R be a ring with involution.The skew Lie product of a, b ∈ R is defined by [a, b] = abba * .In the present paper we study prime ring with involution satisfying identities involving skew Lie product and left centralizers.

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On the traces of certain classes of permuting mappings in rings

2016-01-19

Mohammad Ashraf , Malik Rashid Jamal , Muzibur Rahman Mozumder

A note on Lie ideals of prime rings

2018-03-19

Tsiu‐Kwen Lee , Muzibur Rahman Mozumder

In this paper, we characterize Lie ideals, which are either finitely generated [Formula: see text]-modules or maximal, in (centrally closed) prime rings. As consequences, we extend the results proved in … In this paper, we characterize Lie ideals, which are either finitely generated [Formula: see text]-modules or maximal, in (centrally closed) prime rings. As consequences, we extend the results proved in [1] for finite dimensional central division algebras of characteristic not [Formula: see text] to simple rings of arbitrary characteristic.

Spectrum of the Cozero-Divisor Graph Associated to Ring Zn

2023-10-11

Mohd Zamzuri Ab Rashid , Amal S. Alali , Wasim Ahmed +1 more

Let R be a commutative ring with identity 1≠0 and let Z(R)′ be the set of all non-unit and non-zero elements of ring R. Γ′(R) denotes the cozero-divisor graph of … Let R be a commutative ring with identity 1≠0 and let Z(R)′ be the set of all non-unit and non-zero elements of ring R. Γ′(R) denotes the cozero-divisor graph of R and is an undirected graph with vertex set Z(R)′, w∉zR, and z∉wR if and only if two distinct vertices w and z are adjacent, where qR is the ideal generated by the element q in R. In this article, we investigate the signless Laplacian eigenvalues of the graphs Γ′(Zn). We also show that the cozero-divisor graph Γ′(Zp1p2) is a signless Laplacian integral.

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Signless Laplacian spectrum of the cozero-divisor graph of the commutative ring ℤ𝑛

2023-12-08

Mohd Zamzuri Ab Rashid , Muzibur Rahman Mozumder , Mohd Anwar

A Note on Pair of Left Centralizers in Prime Ring with Involution

2021-04-01

Muzibur Rahman Mozumder , Adnan Abbasi , Nadeem Ahmad Dar +1 more

The purpose of this paper is to study pair of left centralizers in prime rings with involution satisfying certain identities. The purpose of this paper is to study pair of left centralizers in prime rings with involution satisfying certain identities.

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A Characterization of Jordan Left $$^*$$-Centralizers Via Skew Lie and Jordan Products

2022-01-20

Adnan Abbasi , Ci̇hat Abdıoğlu , Shakir Ali +1 more

Note on differential identities on σ-prime rings with involution

2023-01-01

Md Arshad Madni , Muzibur Rahman Mozumder , Wasim Ahmed +2 more

The major goal of this paper is to investigate the structure of [Formula: see text]-prime rings with involution, satisfying certain [Formula: see text]-differential identities involving [Formula: see text]-centralizing and some … The major goal of this paper is to investigate the structure of [Formula: see text]-prime rings with involution, satisfying certain [Formula: see text]-differential identities involving [Formula: see text]-centralizing and some special type of products. We also provide an example which shows that center of [Formula: see text]-prime ring is not free from zero divisors.

On generalized left (alpha, beta)-derivations in rings

2012-12-15

Mohammad Ashraf , Shakir Ali , Nadeem ur Rehman +1 more

On Jordan Triple α-*Centralizers Of Semiprime Rings

2014-03-01

Mohammad Ashraf , Muzibur Rahman Mozumder , Almas Khan

Abstract Let R be a 2-torsion free semiprime ring equipped with an involution *. An additive mapping T : R→R is called a left (resp. right) Jordan α-*centralizer associated with … Abstract Let R be a 2-torsion free semiprime ring equipped with an involution *. An additive mapping T : R→R is called a left (resp. right) Jordan α-*centralizer associated with a function α: R→R if T(x2)=T(x)α(x*) (resp. T(x2)=α(x*)T(x)) holds for all x ∊ R. If T is both left and right Jordan α-* centralizer of R, then it is called Jordan α-* centralizer of R. In the present paper it is shown that if α is an automorphism of R, and T : R→ R is an additive mapping such that 2T(xyx)=T(x) α(y*x*) +α(x*y*)T(x) holds for all x, y ∊ R, then T is a Jordan α-*centralizer of R

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Generalized derivations on Gamma rings

2015-01-01

Ahmad N. Al‐Kenani , Aisha Jabeen , Muzibur Rahman Mozumder

Let M be a 2-torsion free prime -ring and U be a non zero ideal of M such that M admits a generalized derivation F associated with a nonzero derivation … Let M be a 2-torsion free prime -ring and U be a non zero ideal of M such that M admits a generalized derivation F associated with a nonzero derivation d. In the present paper, it is shown that If M satises

A study of generalized derivations in rings

2009-01-01

Muzibur Rahman Mozumder

Tri-Additive Maps and Local Generalized (α, β)-Derivations

2017-11-01

Muzibur Rahman Mozumder , Malik Rashid Jamal

A Characterization of Derivations in Prime Rings with Involution

2019-07-25

Shakir Ali , Muzibur Rahman Mozumder , Adnan Abbasi +1 more

The purpose of this paper is to investigate $*$-differential identities satisfied by pair of derivations on prime rings with involution. In particular, we prove that if a 2-torsion free noncommutative … The purpose of this paper is to investigate $*$-differential identities satisfied by pair of derivations on prime rings with involution. In particular, we prove that if a 2-torsion free noncommutative ring $R$ admit nonzero derivations $d_1, d_2$ such that $[d_1(x), d_2(x^*)]=0$ for all $x\in R$, then $d_1=\lambda d_2$, where $\lambda\in C$. Finally, we provide an example to show that the condition imposed in the hypothesis of our results are necessary.

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A Note on Skew-Commutators with Derivations on Ideals

2020-01-01

Nadeem ur Rehman , Arif Raza , Muzibur Rahman Mozumder

On Commutativity of Prime Rings with Involution Involving Pair of Derivations

2020-01-01

Husain Alhazmi , Shakir Ali , Adnan Abbasi +1 more

On (alpha, beta)-n-derivations and certain n-additive mappings in rings with involution

2015-10-05

Muhammad Ashraf , Mohammad Aslam Siddeeque , Muzibur Rahman Mozumder

Let R be an associative ring with involution ∗. In this paper we introduce the notion of (α,β)∗-n-derivation in R, where α and β are endomorphisms of R. An additive … Let R be an associative ring with involution ∗. In this paper we introduce the notion of (α,β)∗-n-derivation in R, where α and β are endomorphisms of R. An additive mapping x↦x∗ of R into itself is called an involution on R if it satisfies the conditions: (i) (x∗)∗=x, (ii) (xy)∗=y∗x∗ for all x,y∈ R. A ring R equipped with an involution ∗ is called a ∗-ring. In the present paper it is shown that if a ∗-prime ring R admits a nonzero (α,β)∗-n-derivation D such that α is surjective, then R is commutative. Some properties of certain n-additive mappings are also discussed in the setting of ∗-prime rings and semiprime ∗-rings. Further, some related properties of (α,β)∗-n-derivation in semiprime ∗-ring have also been investigated. Besides, we have also constructed several examples throughout the text to justify that various restrictions imposed in the hypotheses of our theorems are not superfluous. Finally a structure theorem for (α,β)∗-n-derivation in a semiprime ∗-ring has been established.

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Characterization of b-generalized Derivations in Rings with Involution

2022-01-01

Adnan Abbasi , Muzibur Rahman Mozumder , Aisha Jabeen

Study of multiplicative derivation and its additivity

2023-01-26

Wasim Ahmed , Muzibur Rahman Mozumder , Arshad Madni

In this paper, we modify the result of M. N. Daif [1] on multiplicative derivations in rings. He showed that the multiplicative derivation is additive by imposing certain conditions on … In this paper, we modify the result of M. N. Daif [1] on multiplicative derivations in rings. He showed that the multiplicative derivation is additive by imposing certain conditions on the ring ℜ. Here, we have proved the above result with lesser conditions than M. N. Daif for getting multiplicative derivation to be additive.

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Nonlinear Skew Lie-Type Derivations on ∗-Algebra

2023-09-06

Md Arshad Madni , Amal S. Alali , Muzibur Rahman Mozumder

Let A be a unital ∗-algebra over the complex fields C. For any H1,H2∈A, a product [H1,H2]•=H1H2−H2H1* is called the skew Lie product. In this article, it is shown that … Let A be a unital ∗-algebra over the complex fields C. For any H1,H2∈A, a product [H1,H2]•=H1H2−H2H1* is called the skew Lie product. In this article, it is shown that if a map ξ : A→A (not necessarily linear) satisfies ξ(Pn(H1,H2,…,Hn))=∑i=1nPn(H1,…,Hi−1,ξ(Hi),Hi+1,…,Hn)(n≥3) for all H1,H2,…,Hn∈A, then ξ is additive. Moreover, if ξ(ie2) is self-adjoint, then ξ is ∗-derivation. As applications, we apply our main result to some special classes of unital ∗-algebras such as prime ∗-algebra, standard operator algebra, factor von Neumann algebra, and von Neumann algebra with no central summands of type I1.

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Characterization of prime rings having involution and centralizers

2023-09-07

Nadeem Ahmad Dar , Adnan Abbasi , Claus Haetinger +2 more

The major goal of this paper is to study the commutativity of prime rings with involution that meet specific identities using left centralizers. The results obtained in this paper are … The major goal of this paper is to study the commutativity of prime rings with involution that meet specific identities using left centralizers. The results obtained in this paper are the generalization of many known theorems. Finally, we provide some examples to show that the conditions imposed in the hypothesis of our results are not superfluous.

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A study of Jordan involution on prime rings involving derivations

2023-01-01

Adnan Abbasi , Abdul Nadim Khan , Muzibur Rahman Mozumder

In this manuscript, we discuss the concept of Jordan involution θ on rings.Moreover, we describe the structure of rings which satisfies some θ-differential identities.Few other related results have also been … In this manuscript, we discuss the concept of Jordan involution θ on rings.Moreover, we describe the structure of rings which satisfies some θ-differential identities.Few other related results have also been discussed.

Commutativity of prime rings with symmetric generalized biderivations

2023-01-01

Muzibur Rahman Mozumder , Wasim Ahmed , Md Arshad Madni

In this manuscript we have generalized the result of B. R. Reddy and C In this manuscript we have generalized the result of B. R. Reddy and C

A note on skew Jordan triple derivations on ∗-rings

2024-01-20

Md Arshad Madni , Ci̇hat Abdıoğlu , Wasim Ahmed +1 more

Let [Formula: see text] be a [Formula: see text]-torsion free unital ∗-ring containing nontrivial symmetric idempotent. In this article, it is shown that if a map [Formula: see text] : … Let [Formula: see text] be a [Formula: see text]-torsion free unital ∗-ring containing nontrivial symmetric idempotent. In this article, it is shown that if a map [Formula: see text] : [Formula: see text] (not necessarily additive) satisfies [Formula: see text] for all [Formula: see text], then [Formula: see text] is additive. Moreover, if [Formula: see text] is self-adjoint, then [Formula: see text] is a ∗-derivation. As an applications, we apply our main result to some special classes of unital ∗-rings and ∗-algebras such as prime ∗-ring, prime ∗-algebra, standard operator algebra, factor von Neumann algebra and von Neumann algebra with no central summands of type [Formula: see text].

A STUDY OF ∗-PRIME RINGS WITH DERIVATIONS

2024-01-01

Adnan Abbasi , Shakir Ali , Abdul Nadim Khan +1 more

This paper's major goal is to describe the structure of the * -prime ring, with the help of three different derivations α, β and γ such that αFurther, some more … This paper's major goal is to describe the structure of the * -prime ring, with the help of three different derivations α, β and γ such that αFurther, some more related results have also been discussed.As applications, classical theorems due to Bell-Daif [6] and Herstein [12] are deduced.

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Characterization of $ (\alpha, \beta) $ Jordan bi-derivations in prime rings

2024-01-01

Wasim Ahmed , Amal S. Alali , Muzibur Rahman Mozumder

<abstract>Let $ \mathfrak{S} $ be a prime ring with automorphisms $ \alpha, \beta $. A bi-additive map $ \mathfrak{D} $ is called an ($ \alpha, \beta $) Jordan bi-derivation if … <abstract>Let $ \mathfrak{S} $ be a prime ring with automorphisms $ \alpha, \beta $. A bi-additive map $ \mathfrak{D} $ is called an ($ \alpha, \beta $) Jordan bi-derivation if $ \mathfrak{D}(k^2, s) = \mathfrak{D}(k, s)\alpha(k) + \beta(k) \mathfrak{D}(k, s) $. In this paper, we find conditions under which a symmetric ($ \alpha, \beta $) Jordan bi-derivation becomes a symmetric ($ \alpha, \beta $) bi-derivation. We also characterize the symmetric $ (\alpha, \beta) $ Jordan bi-derivations.</abstract>

A Study of Central Identities Equipped with Skew Lie Product Involving Generalized Derivations

2024-01-01

Md Arshad Madni , Mohd Shuaib Akhtar , Muzibur Rahman Mozumder

Commutativity of $$\sigma $$-Prime Rings with Generalized Derivation

2024-01-01

Adnan Abbasi , Muzibur Rahman Mozumder

Some Results on Left-sided Ideals of Semiprime Rings with Symmetric $$(\alpha ,\beta )$$ n-Derivations

2024-01-01

Muzibur Rahman Mozumder , Nazia Parveen , Wasim Ahmed

Sombor Index and Sombor Spectrum of Cozero-Divisor Graph of $$\mathbb Z_n$$

2024-04-29

M. M. Anwar , Muzibur Rahman Mozumder , Mohd Zamzuri Ab Rashid +1 more

Characterization of $$(\alpha ,\beta )$$ biderivations in triangular algebras

2024-07-02

Wasim Ahmed , Mohd Shuaib Akhtar , Muzibur Rahman Mozumder

A characterization of σ-prime rings involving generalized derivations

2024-06-24

Md Arshad Madni , Muzibur Rahman Mozumder , Wasim Ahmed +1 more

This paper’s major goal is to work on commutativity of σ-prime rings with second kind involution σ, involving generalized derivation satisfy the certain differential identities. Finally, we provide some examples … This paper’s major goal is to work on commutativity of σ-prime rings with second kind involution σ, involving generalized derivation satisfy the certain differential identities. Finally, we provide some examples to demonstrate that the conditions assumed in our results are not unnecessary

Nonlinear mixed Jordan-type derivations on *-algebras

2024-11-14

Nadeem ur Rehman , Md Arshad Madni , Muzibur Rahman Mozumder

On Lie Ideals with Generalized Homoderivations in Prime Rings

2025-01-01

Wasim Ahmed , Muzibur Rahman Mozumder

A Note on Differential Identities in $$\sigma $$-Prime Ring with Generalized Derivations

2025-01-01

Md Arshad Madni , Muzibur Rahman Mozumder

Exploring Aα spectrum of the weakly zero-divisor graph of the ring ℤn

2025-02-28

Muzibur Rahman Mozumder , Mohd Zamzuri Ab Rashid , Asif Ali Khan

Discrete Mathematics, Algorithms and ApplicationsAccepted Papers No AccessExploring AαAα spectrum of the weakly zero-divisor graph of the ring ZnℤnMuzibur Rahman Mozumder, Mohd Rashid, and Asif Imtiyaz Ahmad KhanMuzibur Rahman Mozumder, … Discrete Mathematics, Algorithms and ApplicationsAccepted Papers No AccessExploring AαAα spectrum of the weakly zero-divisor graph of the ring ZnℤnMuzibur Rahman Mozumder, Mohd Rashid, and Asif Imtiyaz Ahmad KhanMuzibur Rahman Mozumder, Mohd Rashid Search for more papers by this author , and Asif Imtiyaz Ahmad Khanhttps://orcid.org/0009-0008-7947-9566 Search for more papers by this author https://doi.org/10.1142/S179383092550048XCited by:0 (Source: Crossref) PreviousNext AboutFiguresReferencesRelatedDetailsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Cite Recommend Remember to check out the Most Cited Articles! Be inspired by these NEW Mathematics books for inspirations & latest information in your research area! We recommendContinuum dynamics of the intention field under weakly cohesive social interactionPierre Degond, Mathematical Models and Methods in Applied Sciences, 2017Graph-Based Clustering Algorithm for the Internet of VehiclesFan Yang, Journal of Circuits, Systems and Computers, 2022ON THE AMBIPOLAR DIFFUSION AND OTHER ASYMPTOTIC LIMITS OF WEAKLY IONIZED PLASMA FLOWSMathematical Models and Methods in Applied Sciences, 2011Formation and electronic properties of ring-oxidized and ring-reduced radical species of the phthalocyanines and porphyrinsMartin Stillman, Journal of Porphyrins and Phthalocyanines, 2012GLOBAL WEAKLY DISCONTINUOUS SOLUTIONS TO THE MIXED INITIAL–BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMSZHI-QIANG SHAO, Mathematical Models and Methods in Applied Sciences, 2011Comparative overall survival of CDK4/6 inhibitors plus an aromatase inhibitor in HR+/HER2− metastatic breast cancer in the US real-world setting Brought to you by Pfizer Medical Affairs, EM-USA-PLB-0170Brentuximab Vedotin Combination for Relapsed Diffuse Large B-Cell Lymphoma Brought to you by Pfizer Medical Affairs, EM-USA-BVI-0056Powered by Privacy policyGoogle Analytics settings FiguresReferencesRelatedDetailsNone Recommended Recommended The total zero-divisor graph of a commutative ringAlen Ðurić, Sara Jevđenić, Polona Oblak, and Nik StoparJournal of Algebra and Its ApplicationsVol. 18, No. 10ZERO-DIVISOR GRAPH OF AN IDEAL OF A NEAR-RINGT. TAMIZH CHELVAM and S. NITHYADiscrete Mathematics, Algorithms and ApplicationsVol. 05, No. 01Strong zero-divisor graph of rings with involutionNana Kumbhar, Anil Khairnar, and B. N. WaphareAsian-European Journal of MathematicsVol. 16, No. 10Pancyclic zero divisor graph over the ring ℤn[i]Ravindra Kumar and Om PrakashDiscrete Mathematics, Algorithms and ApplicationsVol. 14, No. 08The cozero-divisor graph of a noncommutative ringMojgan AfkhamiJournal of Algebra and Its ApplicationsVol. 13, No. 08On Aα spectrum of the zero-divisor graph of the ring ℤnMohammad Ashraf, M. R. Mozumder, M. Rashid, and NazimDiscrete Mathematics, Algorithms and ApplicationsVol. 16, No. 04Zero-divisor graph of semisimple group-ringsKrishnan Paramasivam and K. Muhammed SabeelJournal of Algebra and Its ApplicationsVol. 21, No. 02Line zero divisor graphsZahra BaratiJournal of Algebra and Its ApplicationsVol. 20, No. 09 Accepted Papers Metrics Downloaded 0 times History Received 8 July 2024 Accepted 20 February 2025 PDF download

Characterization of Multiplicative Mixed Jordan-Type Derivations on Ring with Involution

2025-05-01

Md Arshad Madni , Muzibur Rahman Mozumder , Abu Zaid Ansari +1 more

Let $\mathcal{B}$ be a unital $\varnothing$-ring with a $2$-torsion free that contains non-trivial symmetric idempotent. For any $B_1,B_2,B_3,\ldots,B_n \in \mathcal{B}$, a product $B_1 \circ B_2=B_1B_2+B_2B_1$ is called Jordan product and … Let $\mathcal{B}$ be a unital $\varnothing$-ring with a $2$-torsion free that contains non-trivial symmetric idempotent. For any $B_1,B_2,B_3,\ldots,B_n \in \mathcal{B}$, a product $B_1 \circ B_2=B_1B_2+B_2B_1$ is called Jordan product and $B_1 \bullet B_2=B_1B_2+B_2B_1^\varnothing$ is recognized as a skew Jordan product. Characterize mixed Jordan triple product as $Q_3(B_1,B_2,B_3)=B_1 \circ B_2 \bullet B_3$ and mixed Jordan $n$-product as $Q_n(B_1,B_2,\ldots,B_n)=B_1 \circ B_2 \circ \cdots \bullet B_n$ for all integer $n\geq3$. The present paper deals that a mapping which is called multiplicative mixed Jordan $n$-derivation, $\Psi$: $\mathcal{B} \rightarrow \mathcal{B}$ satisfies $\Psi(Q_n(B_1,B_2,\ldots,B_n))=\sum_{i=1}^{n} Q_n(B_1, \ldots, B_{i-1}, \Psi(B_i), B_{i+1}, \ldots,B_n)$ for all $B_1, B_2,\ldots, B_n \in \mathcal{B}$ if and only if $\Psi$ is an additive $\varnothing$-derivation. Finally, primary outcome is applicable in various specific categories of unital $\varnothing$-rings and $\varnothing$-algebras including prime $\varnothing$-rings, prime $\varnothing$-algebras and factor von Neumann algebras.

Characterization of Multiplicative Mixed Jordan-Type Derivations on Ring with Involution

2025-05-01

Md Arshad Madni , Muzibur Rahman Mozumder , Abu Zaid Ansari +1 more

Exploring Aα spectrum of the weakly zero-divisor graph of the ring ℤn

2025-02-28

Muzibur Rahman Mozumder , Mohd Zamzuri Ab Rashid , Asif Ali Khan

On Lie Ideals with Generalized Homoderivations in Prime Rings

2025-01-01

Wasim Ahmed , Muzibur Rahman Mozumder

A Note on Differential Identities in $$\sigma $$-Prime Ring with Generalized Derivations

2025-01-01

Md Arshad Madni , Muzibur Rahman Mozumder

Nonlinear mixed Jordan-type derivations on *-algebras

2024-11-14

Nadeem ur Rehman , Md Arshad Madni , Muzibur Rahman Mozumder

Characterization of $$(\alpha ,\beta )$$ biderivations in triangular algebras

2024-07-02

Wasim Ahmed , Mohd Shuaib Akhtar , Muzibur Rahman Mozumder

A characterization of σ-prime rings involving generalized derivations

2024-06-24

Md Arshad Madni , Muzibur Rahman Mozumder , Wasim Ahmed +1 more

Sombor Index and Sombor Spectrum of Cozero-Divisor Graph of $$\mathbb Z_n$$

2024-04-29

M. M. Anwar , Muzibur Rahman Mozumder , Mohd Zamzuri Ab Rashid +1 more

A note on skew Jordan triple derivations on ∗-rings

2024-01-20

Md Arshad Madni , Ci̇hat Abdıoğlu , Wasim Ahmed +1 more

A STUDY OF ∗-PRIME RINGS WITH DERIVATIONS

2024-01-01

Adnan Abbasi , Shakir Ali , Abdul Nadim Khan +1 more

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Characterization of $ (\alpha, \beta) $ Jordan bi-derivations in prime rings

2024-01-01

Wasim Ahmed , Amal S. Alali , Muzibur Rahman Mozumder

A Study of Central Identities Equipped with Skew Lie Product Involving Generalized Derivations

2024-01-01

Md Arshad Madni , Mohd Shuaib Akhtar , Muzibur Rahman Mozumder

Commutativity of $$\sigma $$-Prime Rings with Generalized Derivation

2024-01-01

Adnan Abbasi , Muzibur Rahman Mozumder

Some Results on Left-sided Ideals of Semiprime Rings with Symmetric $$(\alpha ,\beta )$$ n-Derivations

2024-01-01

Muzibur Rahman Mozumder , Nazia Parveen , Wasim Ahmed

Signless Laplacian spectrum of the cozero-divisor graph of the commutative ring ℤ𝑛

2023-12-08

Mohd Zamzuri Ab Rashid , Muzibur Rahman Mozumder , Mohd Anwar

Spectrum of the Cozero-Divisor Graph Associated to Ring Zn

2023-10-11

Mohd Zamzuri Ab Rashid , Amal S. Alali , Wasim Ahmed +1 more

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Characterization of prime rings having involution and centralizers

2023-09-07

Nadeem Ahmad Dar , Adnan Abbasi , Claus Haetinger +2 more

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Nonlinear Skew Lie-Type Derivations on ∗-Algebra

2023-09-06

Md Arshad Madni , Amal S. Alali , Muzibur Rahman Mozumder

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Study of multiplicative derivation and its additivity

2023-01-26

Wasim Ahmed , Muzibur Rahman Mozumder , Arshad Madni

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Note on differential identities on σ-prime rings with involution

2023-01-01

Md Arshad Madni , Muzibur Rahman Mozumder , Wasim Ahmed +2 more

A study of Jordan involution on prime rings involving derivations

2023-01-01

Adnan Abbasi , Abdul Nadim Khan , Muzibur Rahman Mozumder

Commutativity of prime rings with symmetric generalized biderivations

2023-01-01

Muzibur Rahman Mozumder , Wasim Ahmed , Md Arshad Madni

In this manuscript we have generalized the result of B. R. Reddy and C In this manuscript we have generalized the result of B. R. Reddy and C

A Characterization of Jordan Left $$^*$$-Centralizers Via Skew Lie and Jordan Products

2022-01-20

Adnan Abbasi , Ci̇hat Abdıoğlu , Shakir Ali +1 more

Characterization of b-generalized Derivations in Rings with Involution

2022-01-01

Adnan Abbasi , Muzibur Rahman Mozumder , Aisha Jabeen

A Note on Pair of Left Centralizers in Prime Ring with Involution

2021-04-01

Muzibur Rahman Mozumder , Adnan Abbasi , Nadeem Ahmad Dar +1 more

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A note on skew Lie product of prime ring with involution

2020-01-01

Adnan Abbasi , Muzibur Rahman Mozumder , Nadeem Ahmad Dar

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A Note on Skew-Commutators with Derivations on Ideals

2020-01-01

Nadeem ur Rehman , Arif Raza , Muzibur Rahman Mozumder

On Commutativity of Prime Rings with Involution Involving Pair of Derivations

2020-01-01

Husain Alhazmi , Shakir Ali , Adnan Abbasi +1 more

A Characterization of Derivations in Prime Rings with Involution

2019-07-25

Shakir Ali , Muzibur Rahman Mozumder , Adnan Abbasi +1 more

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A note on Lie ideals of prime rings

2018-03-19

Tsiu‐Kwen Lee , Muzibur Rahman Mozumder

Tri-Additive Maps and Local Generalized (α, β)-Derivations

2017-11-01

Muzibur Rahman Mozumder , Malik Rashid Jamal

On the traces of certain classes of permuting mappings in rings

2016-01-19

Mohammad Ashraf , Malik Rashid Jamal , Muzibur Rahman Mozumder

On (alpha, beta)-n-derivations and certain n-additive mappings in rings with involution

2015-10-05

Muhammad Ashraf , Mohammad Aslam Siddeeque , Muzibur Rahman Mozumder

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Generalized derivations on Gamma rings

2015-01-01

Ahmad N. Al‐Kenani , Aisha Jabeen , Muzibur Rahman Mozumder

On Jordan Triple α-*Centralizers Of Semiprime Rings

2014-03-01

Mohammad Ashraf , Muzibur Rahman Mozumder , Almas Khan

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MAPS ACTING ON SOME ZERO PRODUCTS

2014-01-01

Hung‐Yuan Chen , Kun-Shan Liu , Muzibur Rahman Mozumder

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On generalized left (alpha, beta)-derivations in rings

2012-12-15

Mohammad Ashraf , Shakir Ali , Nadeem ur Rehman +1 more

ON GENERALIZED (σ, τ)-BIDERIVATIONS IN RINGS

2011-09-01

Mohammad Ashraf , Nadeem ur Rehman , Shakir Ali +1 more

On Semiprime Rings with Generalized Derivations

2010-08-13

Nadeem ur Rehman , Mohammad Ashraf , Shakir Ali +1 more

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A study of generalized derivations in rings

2009-01-01

Muzibur Rahman Mozumder

Coauthor	Papers Together
Adnan Abbasi	11
Wasim Ahmed	10
Md Arshad Madni	9
Shakir Ali	7
Mohammad Ashraf	5
Nadeem ur Rehman	5
Mohd Zamzuri Ab Rashid	4
Nadeem Ahmad Dar	3
Amal S. Alali	3
Mohd Shuaib Akhtar	2
Abdul Nadim Khan	2
Arshad Madni	2
Ci̇hat Abdıoğlu	2
Aisha Jabeen	2
Malik Rashid Jamal	2
Abu Zaid Ansari	2
Arif Raza	2
Tsiu‐Kwen Lee	1
Aftab Hussain Shah	1
Hung‐Yuan Chen	1
M. M. Anwar	1
Mohd Anwar	1
Kun-Shan Liu	1
Moharram Khan	1
Faiza Shujat	1
Asif Ali Khan	1
Muhammad Ashraf	1
Almas Khan	1
Nazia Parveen	1
Claus Haetinger	1
Mohammad Aslam Siddeeque	1
A. Ramesh	1
Husain Alhazmi	1
Ahmad N. Al‐Kenani	1

Commutativity theorems in rings with involution

2016-10-07

B. Nejjar , Ali Kacha , Abdellah Mamouni +1 more

In this paper, we investigate commutativity of ring R with involution ∗ which admits a derivation satisfying certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been … In this paper, we investigate commutativity of ring R with involution ∗ which admits a derivation satisfying certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been generalized. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.

On *-centralizing mappings in rings with involution

2014-02-15

Shakir Ali , Nadeem Ahmed Dar

Derivations in prime rings

1957-12-01

Edward C. Posner

iqaqaq)bq + qaqbqaq = 0 iqaqaq)bq + qaqbqaq = 0

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Centralizing Mappings of Prime Rings

1984-03-01

Joseph H. Mayne

Abstract Let R be a prime ring and U be a nonzero ideal or quadratic Jordan ideal of R . If L is a nontrivial automorphism or derivation of R … Abstract Let R be a prime ring and U be a nonzero ideal or quadratic Jordan ideal of R . If L is a nontrivial automorphism or derivation of R such that uL ( u )— L ( u ) u is in the center of R for every u in U , then the ring R is commutative.

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On Commutativity of Rings With Derivations

2002-08-01

Mohammad Ashraf , Nadeem ur Rehman

Let R be a ring and d : R → R a derivation of R. In the present paper we investigate commutativity of R satisfying any one of the properties … Let R be a ring and d : R → R a derivation of R. In the present paper we investigate commutativity of R satisfying any one of the properties (i)d([x,y]) = [x,y], (ii)d(x o y) = xoy, (iii)d(x) o d(y) = 0, or (iv)d(x) o d(y) = x o y, for all x, y in some apropriate subset of R.

Derivations in Prime Rings

1957-12-01

Edward C. Posner

iqaqaq)bq + qaqbqaq = 0 iqaqaq)bq + qaqbqaq = 0

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Additive maps on prime and semiprime rings with involution

2019-12-18

Adel Alahmadi , Husain Alhazmi , Shakir Ali +2 more

Let $R$ be an associative ring. An additive map $x\mapsto x^*$ of $R$ into itself is called an involution if (i) $(xy)^*=y^*x^*$ and (ii) $(x^*)^*=x$ hold for all $x\in R$. … Let $R$ be an associative ring. An additive map $x\mapsto x^*$ of $R$ into itself is called an involution if (i) $(xy)^*=y^*x^*$ and (ii) $(x^*)^*=x$ hold for all $x\in R$. The main purpose of this paper is to study some additive mappings on prime and semiprime rings with involution. Moreover, some examples are given to demonstrate that the restrictions imposed on the hypothesis of the various results are not superfluous.

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Commutativity results for semiprime rings with derivations

1996-10-10

Mohammad Nagy Daif

We extend a result of Herstein concerning a derivation d on a prime ring R satisfying [ d ( x ), d ( y )] = 0 for all x … We extend a result of Herstein concerning a derivation d on a prime ring R satisfying [ d ( x ), d ( y )] = 0 for all x , y ∈ R , to the case of semiprime rings. An extension of this result is proved for a two‐sided ideal but is shown to be not true for a one‐sided ideal. Some of our recent results dealing with U * ‐ and U ** ‐ derivations on a prime ring are extended to semiprime rings. Finally, we obtain a result on semiprime rings for which d ( x y ) = d ( y x ) for all x , y in some ideal U .

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Differential identities, Lie ideals, and Posner’s theorems

1988-10-01

Charles Lanski

Two well-known results of E. C. Posner state that the composition of two nonzero derivations of a prime ring cannot be a nonzero derivation, and that in a prime ring, … Two well-known results of E. C. Posner state that the composition of two nonzero derivations of a prime ring cannot be a nonzero derivation, and that in a prime ring, if the commutator of each element and its image under a nonzero derivation is central, then the ring is commutative.Our purpose is to show how the theory of differential identities can be used to obtain these results and their generalizations to Lie ideals and to rings with involution.

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On derivations and commutativity in prime rings

1995-12-01

Howard E. Bell , M. N. Daif

Generalized derivations centralizing on Jordanideals of rings with involution

2014-01-01

Lahcen Oukhtite , Abdellah Mamouni

A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend Posner's … A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend Posner's result to generalized derivations centralizing on Jordan ideals of rings with involution and discuss the related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.

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Centralizing Mappings of Semiprime Rings

1987-03-01

Howard E. Bell , Wallace S. Martindale

Abstract Let R be a ring with center Z, and S a nonempty subset of R . A mapping F from R to R is called centralizing on S if … Abstract Let R be a ring with center Z, and S a nonempty subset of R . A mapping F from R to R is called centralizing on S if [ x, F(x) ] ∊ Z for all x ∊ S . We show that a semiprime ring R must have a nontrivial central ideal if it admits an appropriate endomorphism or derivation which is centralizing on some nontrivial one-sided ideal. Under similar hypotheses, we prove commutativity in prime rings.

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Left centralizers on rings that are not semiprime

2011-09-26

Irvin Roy Hentzel , M. S. Tammam El-Sayiad

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On $*$-commuting mappings and derivations in rings with involution

2016-01-01

Nadeem Ahmad Dar , Shakir Ali

Let $R$ be a ring with involution $*$. A mapping $f:R\rightarrow R$ is said to be $*$-commuting on $R$ if $[f(x),x^*]=0$ holds for all $x\in R$. The purpose of this … Let $R$ be a ring with involution $*$. A mapping $f:R\rightarrow R$ is said to be $*$-commuting on $R$ if $[f(x),x^*]=0$ holds for all $x\in R$. The purpose of this paper is to describe the structure of a pair of additive mappings that are $*$-commuting on a semiprime ring with involution. Furthermore, we study the commutativity of prime rings with involution satisfying any one of the following conditions: (i) $[d(x),d(x^*)]=0,$ (ii) $d(x)\circ d(x^*)=0$, (iii) $d([x,x^*])\pm [x,x^*]=0$ (iv) $d(x\circ x^*)\pm (x\circ x^*)=0,$ (v) $d([x,x^*])\pm (x\circ x^*)=0$, (vi) $d(x\circ x^*)\pm [x,x^*]=0$, where $d$ is a nonzero derivation of $R$. Finally, an example is given to demonstrate that the condition of the second kind of involution is not superfluous.

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Centralizers on semiprime rings

2001-01-01

Joso Vukman

The main result: Let R be a 2-torsion free semiprime ring and let T : R ! R be an additive mapping. Suppose that T(xyx) = xT(y)x holds for all … The main result: Let R be a 2-torsion free semiprime ring and let T : R ! R be an additive mapping. Suppose that T(xyx) = xT(y)x holds for all x, y 2 R. In this case T is a centralizer.

Posner's First Theorem for *-ideals in Prime Rings with Involution

2016-06-23

Mohammad Ashraf , Mohammad Aslam Siddeeque

Posner's first theorem states that if R is a prime ring of characteristic different from two, d 1 and d 2 are derivations on R such that the iterate d … Posner's first theorem states that if R is a prime ring of characteristic different from two, d 1 and d 2 are derivations on R such that the iterate d 1 d 2 is also a derivation of R, then at least one of d 1 , d 2 is zero.In the present paper we extend this result to * -prime rings of characteristic different from two.* -ideal of R if I * = I.Let R be a * -prime ring, a ∈ R and aRa = {0}.This implies that aRaRa * = {0} also.Now * -primeness of R insures that a = 0 or aRa * = {0}.aRa * = {0} together with aRa = {0} gives us a = 0. Thus we conclude that every * -prime ring is a semiprime ring.An additive mapping d : R -→ R is said to be a derivation on R if d(xy) = d(x)y + xd(y) holds for all x, y ∈ R. Let I be a nonzero ideal of R. Then an additive mapping d : I -→ R is called a derivation from I to R if d(xy) = d(x)y +

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A note on automorphisms of prime and semiprime rings

2005-01-01

Asif Ali , Muhammad Yasen

Let f be a centralizing automorphism of a semiprime ring R. Then for all x ∈ R (f (x) -x) ∈ Z(R); that is the mapping f -1 maps R … Let f be a centralizing automorphism of a semiprime ring R. Then for all x ∈ R (f (x) -x) ∈ Z(R); that is the mapping f -1 maps R into its centre.

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Adjacency matrices of zero-divisor graphs of integers modulon

2015-09-28

Matthew Young

Adjacency matrices of zero-divisor graphs of integers modulo n Matthew Young (Communicated by Kenneth S. Berenhaut Adjacency matrices of zero-divisor graphs of integers modulo n Matthew Young (Communicated by Kenneth S. Berenhaut

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Centralizing Mappings and Derivations in Prime Rings

1993-04-01

Matej Brešar

On the distance of the composition of two derivations to the generalized derivations

1991-01-01

Matej Brešar

A well-known theorem of E. Posner [10] states that if the composition d 1 d 2 of derivations d 1 d 2 of a prime ring A of characteristic not … A well-known theorem of E. Posner [10] states that if the composition d 1 d 2 of derivations d 1 d 2 of a prime ring A of characteristic not 2 is a derivation, then either d 1 = 0 or d 2 = 0. A number of authors have generalized this theorem in several ways (see e.g. [1], [2], and [5], where further references can be found). Under stronger assumptions when A is the algebra of all bounded linear operators on a Banach space (resp. Hilbert space), Posner's theorem was reproved in [3] (resp. [12]). Recently, M. Mathieu [8] extended Posner's theorem to arbitrary C * -algebras.

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On centralizers of semiprime rings with involution

2006-02-01

Joso Vukman , Irena Kosi-Ulbl

Let R be a 2-torsion free semiprime *-ring and let T : R ? R be an additive mapping such that T ( xx *)= T ( x ) x … Let R be a 2-torsion free semiprime *-ring and let T : R ? R be an additive mapping such that T ( xx *)= T ( x ) x * is fulfilled for all x ? R . In this case T ( xy )= T ( x ) y holds for all pairs x,y ? R .

SOME RESULTS ON COZERO-DIVISOR GRAPH OF A COMMUTATIVE RING

2013-07-31

Saieed Akbari , Fereydoon Alizadeh , S. Khojasteh

Let R be a commutative ring with unity. The cozero-divisor graph of R denoted by Γ′(R) is a graph with the vertex set W*(R), where W*(R) is the set of … Let R be a commutative ring with unity. The cozero-divisor graph of R denoted by Γ′(R) is a graph with the vertex set W*(R), where W*(R) is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b are adjacent if and only if a ∉ Rb and b ∉ Ra. In this paper, we show that if Γ′(R) is a forest, then Γ′(R) is a union of isolated vertices or a star. Also, we prove that if Γ′(R) is a forest with at least one edge, then R ≅ ℤ 2 ⊕ F, where F is a field. Among other results, it is shown that for every commutative ring R, diam (Γ′(R[x])) = 2. We prove that if R is a field, then Γ′(R[[x]]) is totally disconnected. Also, we prove that if (R, m) is a commutative local ring and m ≠ 0, then diam (Γ′(R[[x]])) ≤ 3. Finally, it is proved that if R is a commutative non-local ring, then diam (Γ′(R[[x]])) ≤ 3.

Signless Laplacian and normalized Laplacian on the H-join operation of graphs

2014-04-30

Baofeng Wu , Yuan-Yuan Lou , Changxiang He

In this paper, we consider a generalized join operation, that is, the H-join on graphs, where H is an arbitrary graph. In terms of the signless Laplacian and the normalized … In this paper, we consider a generalized join operation, that is, the H-join on graphs, where H is an arbitrary graph. In terms of the signless Laplacian and the normalized Laplacian, we determine the spectra of the graphs obtained by this operation on regular graphs. Some additional consequences on the spectral radius, integral graphs and cospectral graphs, etc. are also obtained.

On the cozero-divisor graphs associated to rings

2022-08-19

Praveen Mathil , Barkha Baloda , Jitender Kumar

Let R be a ring with unity. The cozero-divisor graph of a ring R, denoted by Γ′(R), is an undirected simple graph whose vertices are the set of all non-zero … Let R be a ring with unity. The cozero-divisor graph of a ring R, denoted by Γ′(R), is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of R, and two distinct vertices x and y are adjacent if and only if x∉Ry and y∉Rx. In this paper, first we study the Laplacian spectrum of Γ′(Zn). We show that the graph Γ′(Zpq) is Laplacian integral. Further, we obtain the Laplacian spectrum of Γ′(Zn) for n=pn1qn2, where n1,n2∈N and p, q are distinct primes. In order to study the Laplacian spectral radius and algebraic connectivity of Γ′(Zn), we characterized the values of n for which the Laplacian spectral radius is equal to the order of Γ′(Zn). Moreover, the values of n for which the algebraic connectivity and vertex connectivity of Γ′(Zn) coincide are also described. At the final part of this paper, we obtain the Wiener index of Γ′(Zn) for arbitrary n.

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Prime rings satisfying a generalized polynomial identity

1969-08-01

Wallace S. Martindale

Remarks on derivations on semiprime rings

1991-05-10

M. N. Daif , Howard E. Bell

We prove that a semiprime ring R must be commutative if it admits a derivation d such that (i) x y + d ( x y ) = y x … We prove that a semiprime ring R must be commutative if it admits a derivation d such that (i) x y + d ( x y ) = y x + d ( y x ) for all x , y in R , or (ii) x y − d ( x y ) = y x − d ( y x ) for all x , y in R . In the event that R is prime, (i) or (ii) need only be assumed for all x , y in some nonzero ideal of R .

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On centralizers of semiprime rings

1991-01-01

Borut Zalar

Let $\Cal K$ be a semiprime ring and $T:\Cal K\rightarrow \Cal K$ an additive mapping such that $T(x^2)=T(x)x$ holds for all $x\in \Cal K$. Then $T$ is a left centralizer … Let $\Cal K$ be a semiprime ring and $T:\Cal K\rightarrow \Cal K$ an additive mapping such that $T(x^2)=T(x)x$ holds for all $x\in \Cal K$. Then $T$ is a left centralizer of $\Cal K$. It is also proved that Jordan centralizers and centralizers of $\Cal K$ coincide.

On Jordan *-derivations and an application

1990-01-01

Peter Šemrl

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An identity related to centralizers in semiprime rings

1999-01-01

Joso Vukman

Generalized Derivations in Rings

2025-03-18

Shakir Ali , Muhammad Ashraf , Vincenzo De Filippis +2 more

The objective of this paper is to define the notions of generalized -derivation & generalized reverse -derivation, and to prove some theorems involving these mappings. As an application, generalized -derivations … The objective of this paper is to define the notions of generalized -derivation & generalized reverse -derivation, and to prove some theorems involving these mappings. As an application, generalized -derivations of C -algebra are characterized.

On Commutativity and Strong Commutativity-Preserving Maps

1994-12-01

Howard E. Bell , M. N. Daif

Abstract If R is a ring and S ⊆ R , a mapping f:R —> R is called strong commutativity- preserving (scp) on S if [x, y] = [f(x),f(y)] for … Abstract If R is a ring and S ⊆ R , a mapping f:R —> R is called strong commutativity- preserving (scp) on S if [x, y] = [f(x),f(y)] for all x,y € S . We investigate commutativity in prime and semiprime rings admitting a derivation or an endomorphism which is scp on a nonzero right ideal.

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GPIs having coefficients in Utumi quotient rings

1988-01-01

Chen-Lian Chuang

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a prime ring and let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper U"> <mml:semantics> <mml:mi>U</mml:mi> <mml:annotation encoding="application/x-tex">U</mml:annotation> … Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a prime ring and let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper U"> <mml:semantics> <mml:mi>U</mml:mi> <mml:annotation encoding="application/x-tex">U</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be its Utumi quotient ring. We prove the following: (1) If <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> satisfies a GPI having all its coefficients in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper U"> <mml:semantics> <mml:mi>U</mml:mi> <mml:annotation encoding="application/x-tex">U</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> satisfies a GPI having all its coefficients in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. (2) <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper U"> <mml:semantics> <mml:mi>U</mml:mi> <mml:annotation encoding="application/x-tex">U</mml:annotation> </mml:semantics> </mml:math> </inline-formula> satisfy the same GPIs having their coefficients in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper U"> <mml:semantics> <mml:mi>U</mml:mi> <mml:annotation encoding="application/x-tex">U</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.

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Nonlinear skew Jordan derivable maps on factor von Neumann algebras

2016-01-28

Fangjuan Zhang

AbstractLet be a factor von Neumann algebra. Suppose that is a nonlinear skew Jordan derivable map. Then, is an additive -derivation. In particular, if the von Neumann algebra is infinite … AbstractLet be a factor von Neumann algebra. Suppose that is a nonlinear skew Jordan derivable map. Then, is an additive -derivation. In particular, if the von Neumann algebra is infinite type I factors, a concrete characterization of is given.Keywords: skew Jordan derivable map-derivationvon Neumann algebraAMS Subject Classifications: 47B4946L10 NotesNo potential conflict of interest was reported by the author.Additional informationFundingThis research was supported by the National Natural Science Foundation of China [grant number 11402199], [grant number 11426176].

On Commutativity of Rings with Generalized Derivations

2002-01-01

Nadeem ur Rehman

The concept of derivations as well as of generalized inner derivations have been generalized as an additive function F : R → R satisfying F(xy) = F(x)y + xd(y) for … The concept of derivations as well as of generalized inner derivations have been generalized as an additive function F : R → R satisfying F(xy) = F(x)y + xd(y) for all x, y ∈ R, where d is a derivation on R, such a function F is said to be a generalized derivation. In the present paper we have discussed the commutativity of prime rings admitting a generalized derivation F satisfying (i) [F(x), x] = 0, (ii) F([x, y]) = [x, y], and (iii) F(x ◦ y) = x ◦ y for all x, y in some appropriate subset of R.

A Note on Commuting Automorphisms of Rings

1970-01-01

Jiang Luh

"A Note on Commuting Automorphisms of Rings." The American Mathematical Monthly, 77(1), pp. 61–62 "A Note on Commuting Automorphisms of Rings." The American Mathematical Monthly, 77(1), pp. 61–62

Nonlinear *-Lie-type derivations on standard operator algebras

2017-12-15

Weibin Lin

Generalized derivations in rings*

1998-01-01

Bojan Hvala

(1998). Generalized derivations in rings. Communications in Algebra: Vol. 26, No. 4, pp. 1147-1166. (1998). Generalized derivations in rings. Communications in Algebra: Vol. 26, No. 4, pp. 1147-1166.

A note on semiprime rings with derivation

1996-03-03

Motoshi Hongan

Let R be a 2‐torsion free semiprime ring, I a nonzero ideal of R , Z the center of R and D : R → R a derivation. If d … Let R be a 2‐torsion free semiprime ring, I a nonzero ideal of R , Z the center of R and D : R → R a derivation. If d [ x , y ] + [ x , y ] ∈ Z or d [ x , y ] − [ x , y ] ∈ Z for all x , y ∈ I , then R is commutative.

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On derivations and commutativity in prime rings

2004-01-01

Vincenzo De Filippis

Let R be a prime ring of characteristic different from 2, d a nonzero derivation of R , and I a nonzero right ideal of R such that [[ d … Let R be a prime ring of characteristic different from 2, d a nonzero derivation of R , and I a nonzero right ideal of R such that [[ d ( x ), x ], [ d ( y ), y ]] = 0, for all x , y ∈ I . We prove that if [ I , I ] I ≠ 0, then d ( I ) I = 0.

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Nonlinear maps preserving Jordan *-products

2013-07-19

Liqing Dai , Fangyan Lu

Coloring of commutative rings

1988-07-01

István Beck

Left Multipliers and Jordan Ideals in Rings with Involution

2011-01-01

Lahcen Oukhtite

The purpose of this paper is to study left multipliers satisfying certain identities on Jordan ideals of rings with involution. Some well known results characterizing commutativity of prime rings by … The purpose of this paper is to study left multipliers satisfying certain identities on Jordan ideals of rings with involution. Some well known results characterizing commutativity of prime rings by left multipliers have also been extended to Jordan ideals.

Derivations modulo elementary operators

2011-05-25

Chen-Lian Chuang , Tsiu‐Kwen Lee

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Symmetric bi-derivations on prime and semi-prime rings

1989-06-01

Joso Vukman

Lie ideals and derivations of prime rings

1981-07-01

Jeffrey Bergen , I. N. Herstein , Jeanne Wald Kerr

Maps characterized by action on zero products

2004-10-01

M. A. Chebotar , Wen-Fong Ke , Pjek-Hwee Lee

For prime rings containing nontrivial idempotents, we describe the bijective additive maps which preserve zero products.Also, we describe the additive maps which behave like derivations when acting on zero products. For prime rings containing nontrivial idempotents, we describe the bijective additive maps which preserve zero products.Also, we describe the additive maps which behave like derivations when acting on zero products.

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