SU\G(𝔸)/K·U

William C. Waterhouse

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All published works
Action Title Year Authors
+ AUTOMORPHISM GROUP SCHEMES OF SEMISIMPLE 2016 William C. Waterhouse
+ Bhattacharyya’s matrix theorem 2012 William C. Waterhouse
+ Square Root as a Homomorphism 2012 William C. Waterhouse
+ An Urn Problem with Labeled and Unlabeled Balls: 11181. 2007 Angelo J. Christino
William C. Waterhouse
+ Real congruences of complex subspaces of 2×2 symmetric complex matrices 2006 William C. Waterhouse
+ PDF Chat A Quotation from Moliere in Bentham 2005 William C. Waterhouse
+ The structure of alternating-Hamiltonian matrices 2004 William C. Waterhouse
+ Intersections of two cofinite subfields 2004 William C. Waterhouse
+ How many vectors generate maximal cyclic subspaces? 2003 William C. Waterhouse
+ Quadratic Polynomials and Unique Factorization 2002 William C. Waterhouse
+ Quadratic Polynomials and Unique Factorization 2002 William C. Waterhouse
+ Local compactness of Hom (—, H) 2001 Paul R. Chernoff
William C. Waterhouse
+ Cochran's Theorem for Rings 2001 William C. Waterhouse
+ Asymmetric linear correlations of projective planes over fields 2001 William C. Waterhouse
+ Cochran's Theorem for Rings 2001 William C. Waterhouse
+ Nonconstant Functions with Derivative Zero: 10772 2000 William C. Waterhouse
S.R. Butcher
+ On the Ranks of Skew Centrosymmetric Matrices over Finite Fields 1998 William C. Waterhouse
+ Eigenmatrices of a normal matrix 1997 William C. Waterhouse
+ Some Boundary Problems with Even or Odd Solutions 1996 William C. Waterhouse
+ A Conditional Trace Inequality (Paul A. Roediger) 1996 Robert R. Burnside
William C. Waterhouse
+ PDF Chat Automorphism Group Schemes of Basic Matrix Invariants 1995 William C. Waterhouse
+ Polarization Formulas over Separable Algebras 1995 William C. Waterhouse
+ PDF Chat Automorphism group schemes of basic matrix invariants 1995 William C. Waterhouse
+ Geometrically reductive affine group schemes 1994 William C. Waterhouse
+ Linear operators on Clifford algebras 1994 William C. Waterhouse
+ PDF Chat The Normal Closures of Certain Kummer Extensions 1994 William C. Waterhouse
+ A unified version of the primitive and normal basis theorems 1994 William C. Waterhouse
+ The degrees of the cyclotomic extension fields 1993 William C. Waterhouse
+ Automorphism Group Schemes of Semisimple Cosemisimple Hopf Algebras 1993 William C. Waterhouse
+ Harmonic means and diophantus I.39 1993 William C. Waterhouse
+ Retractions of separable commutative algebras 1993 William C. Waterhouse
+ Extensions of complex number multiplication to 4-tuples 1992 William C. Waterhouse
+ Displacement operators relative to group matrices 1992 William C. Waterhouse
+ Continued Fractions and Pythagorean Triples 1992 William C. Waterhouse
+ Maximal orders in nonassociative quaternion algebras 1992 Hee Jung Lee
William C. Waterhouse
+ Differentiable functions on algebras and the equation grad (<i>w</i>) = <i>M</i> grad (<i>v</i>) 1992 William C. Waterhouse
+ PDF Chat Automorphisms and Twisted Forms of Generalized Witt Lie Algebras 1991 William C. Waterhouse
+ An elementary interpretation of entry 12 in Gauss's Tagebuch 1991 William C. Waterhouse
+ A local determination theorem for finite principal homogeneous spaces 1991 William C. Waterhouse
+ PDF Chat Automorphisms and twisted forms of generalized Witt Lie algebras 1991 William C. Waterhouse
+ Classifying nonsingular quadratic forms of rank three 1990 William C. Waterhouse
+ Gauss's first argument for least squares 1990 William C. Waterhouse
+ The absolute-value estimate for symmetric multilinear forms 1990 William C. Waterhouse
+ The determination of all Carlitz sets 1989 William C. Waterhouse
+ Linear transformations preserving symmetric rank one matrices 1989 William C. Waterhouse
+ Automorphisms of the Bruhat order on Coxeter Groups 1989 William C. Waterhouse
+ Two Elementary Proofs of an Inequality (and 1½ Better Ones) 1989 William C. Waterhouse
+ Two Elementary Proofs of an Inequality (and 1½ Better Ones) 1989 William C. Waterhouse
+ Two generators for the general linear groups over finite fields 1989 William C. Waterhouse
+ A tiny note on Gauss's Lemma 1988 William C. Waterhouse
+ PDF Chat Tame Objects for Finite Commutative Hopf Algebras 1988 William C. Waterhouse
+ Sums of weight vectors and sums of semilinear functions 1988 Konrad J. Heuvers
William C. Waterhouse
+ PDF Chat Tame objects for finite commutative Hopf algebras 1988 William C. Waterhouse
+ A unified Kummer-Artin-Schreier sequence 1987 William C. Waterhouse
+ Automorphisms of det(Xij): The group scheme approach 1987 William C. Waterhouse
+ Elementary divisors of s-symmetric matrices 1987 William C. Waterhouse
+ The Structure of Monomial Circulant Matrices 1987 William C. Waterhouse
+ How often do determinants over finite fields vanish? 1987 William C. Waterhouse
+ A note on fan's identity for symmetric bilinear forms 1987 William C. Waterhouse
+ The g-circulant solutions of Am=λJ 1987 S.L. Ma
William C. Waterhouse
+ Scaled trace forms over number fields 1986 William C. Waterhouse
+ A neglected note showing Gauss at work 1986 William C. Waterhouse
+ Positivity properties in pencils of matrices† 1986 William C. Waterhouse
+ Why Square Roots are Irrational 1986 William C. Waterhouse
+ Why Square Roots are Irrational 1986 William C. Waterhouse
+ Linear transformations on self-adjoint matrices: the preservation of rank-one-plus-scalar 1986 William C. Waterhouse
+ Circulant-style matrices closed under multiplication 1985 William C. Waterhouse
+ On linear transformations preserving rank one matrices over commutative rings 1985 William C. Waterhouse
+ PDF Chat Symmetric determinants and Jordan norm similarities in characteristic 2 1985 William C. Waterhouse
+ Similarity of matrices under SL(<i>n</i>,<i>K</i>) 1984 William C. Waterhouse
+ The asymptotic density of supersingular Fermat varieties 1984 Wolfgang Schwarz
William C. Waterhouse
+ A note by Gauss referring to ideals? 1984 William C. Waterhouse
+ The density of supersingular Fermat varieties 1984 William C. Waterhouse
+ PDF Chat Composition and genera of norm-type forms 1984 William C. Waterhouse
+ A conjectured property of Hermitian pencils 1983 William C. Waterhouse
+ Do Symmetric Problems Have Symmetric Solutions? 1983 William C. Waterhouse
+ 67.21 Visualising Cramer’s rule 1983 William C. Waterhouse
+ Do Symmetric Problems Have Symmetric Solutions? 1983 William C. Waterhouse
+ Invertibility of linear maps preserving matrix invariants 1983 William C. Waterhouse
+ Quantifier problems beyond uniformity 1983 William C. Waterhouse
+ Real classification of complex quadrics 1982 William C. Waterhouse
+ PDF Chat Automorphisms of quotients of ΠGL(<i>n</i><sub><i>i</i></sub>) 1982 William C. Waterhouse
+ PDF Chat The Unit Groups of Affine Algebraic Monoids 1982 William C. Waterhouse
+ PDF Chat Polynomial group laws over valuation rings 1982 William C. Waterhouse
+ Linear maps preserving reduced norms 1982 William C. Waterhouse
+ PDF Chat The unit groups of affine algebraic monoids 1982 William C. Waterhouse
+ PDF Chat Book Review: Formal groups and applications 1982 William C. Waterhouse
+ Review: Michiel Hazewinkel, Formal groups and applications 1982 William C. Waterhouse
+ The module structure of certain hopf algebra extensions 1982 William C. Waterhouse
+ PDF Chat Projective Modules Over Rings with Many Units 1981 B. R. McDonald
William C. Waterhouse
+ PDF Chat Projective modules over rings with many units 1981 Bernard R. McDonald
William C. Waterhouse
+ Abstract homomorphisms of algebraic groups: problems and bibliography 1981 Donald G. James
William C. Waterhouse
Boris Weisfeiler
+ One-dimensional affine group schemes 1980 William C. Waterhouse
Boris Weisfeiler
+ PDF Chat Commutative polynomial group laws over valuation rings 1980 William C. Waterhouse
+ Subgroups of ax + b and the Splitting of Triangular Group Schemes 1980 William C. Waterhouse
+ Automorphisms of GL n (R) 1980 William C. Waterhouse
+ PDF Chat Automorphisms of 𝐺𝐿_{𝑛}(𝑅) 1980 William C. Waterhouse
+ PDF Chat Subgroups of 𝑎𝑥+𝑏 and the splitting of triangular group schemes 1980 William C. Waterhouse
+ Gauss on infinity 1979 William C. Waterhouse
+ The Normal Basis Theorem 1979 William C. Waterhouse
+ The Normal Basis Theorem 1979 William C. Waterhouse
+ Affine Group Schemes 1979 William C. Waterhouse
+ Algebraic Matrix Groups 1979 William C. Waterhouse
+ Groups of Multiplicative Type 1979 William C. Waterhouse
+ Nilpotent and Solvable Groups 1979 William C. Waterhouse
+ Quotient Maps 1979 William C. Waterhouse
+ Unipotent Groups 1979 William C. Waterhouse
+ Lie Algebras 1979 William C. Waterhouse
+ Jordan Decomposition 1979 William C. Waterhouse
+ Descent Theory Formalism 1979 William C. Waterhouse
+ Affine Group Schemes: Examples 1979 William C. Waterhouse
+ Introduction to Affine Group Schemes 1979 William C. Waterhouse
+ Construction of Quotients 1979 William C. Waterhouse
+ Faithful Flatness of Hopf Algebras 1979 William C. Waterhouse
+ Irreducible and Connected Components 1979 William C. Waterhouse
+ PDF Chat A Probable Hasse Principle for Pencils of Quadrics 1978 William C. Waterhouse
+ PDF Chat A probable Hasse principle for pencils of quadrics 1978 William C. Waterhouse
+ PDF Chat Class Groups of Rings of Invariants 1977 William C. Waterhouse
+ A Nonsymmetric Hasse-Minkowski Theorem 1977 William C. Waterhouse
+ PDF Chat Pairs of symmetric bilinear forms in characteristic 2 1977 William C. Waterhouse
+ PDF Chat Class groups of rings of invariants 1977 William C. Waterhouse
+ Self-adjoint operators and formally real fields 1976 William C. Waterhouse
+ Pairs of quadratic forms 1976 William C. Waterhouse
+ Notes toward higher differential algebra 1976 William C. Waterhouse
+ Antipodes and group-likes in finite Hopf algebras 1975 William C. Waterhouse
+ PDF Chat The Structure of Inseparable Field Extensions 1975 William C. Waterhouse
+ PDF Chat Basically bounded functors and flat sheaves 1975 William C. Waterhouse
+ PDF Chat The structure of inseparable field extensions 1975 William C. Waterhouse
+ PDF Chat The heights of formal 𝐴-modules 1974 William C. Waterhouse
+ Shorter Notes: Profinite Groups are Galois Groups 1974 William C. Waterhouse
+ PDF Chat Profinite groups are Galois groups 1974 William C. Waterhouse
+ PDF Chat A non-criterion for central simple algebras 1973 William C. Waterhouse
+ Pieces of eight in class groups of quadratic fields 1973 William C. Waterhouse
+ Moore's theorem on uniqueness of reciprocity laws 1972 Stephen U. Chase
William C. Waterhouse
+ PDF Chat An empty inverse limit 1972 William C. Waterhouse
+ The discovery of the regular solids 1972 William C. Waterhouse
+ On p-Divisible Groups over Complete Valuation Rings 1972 William C. Waterhouse
+ Extreme and Mean Ratio in Vergil? 1972 William C. Waterhouse
+ PDF Chat Divisor classes in pseudo Galois extensions 1971 William C. Waterhouse
+ Automorphism schemes and forms of Witt Lie algebras 1971 William C. Waterhouse
+ PDF Chat Principal homogeneous spaces and group scheme extensions 1971 William C. Waterhouse
+ PDF Chat Principal Homogeneous Spaces and Group Scheme Extensions 1971 William C. Waterhouse
+ PDF Chat Abelian varieties over finite fields 1971 William C. Waterhouse
J. S. Milne
+ PDF Chat A classification of almost full formal groups 1969 William C. Waterhouse
+ PDF Chat A Classification of Almost Full Formal Groups 1969 William C. Waterhouse
+ PDF Chat Abelian varieties over finite fields 1969 William C. Waterhouse
+ PDF Chat The Stone-Weierstrass theorem for valuable fields 1968 Paul R. Chernoff
Richard Rasala
William C. Waterhouse
+ PDF Chat Dual groups of vector spaces 1968 William C. Waterhouse
Common Coauthors
Coauthor Papers Together
Paul R. Chernoff 2
Boris Weisfeiler 2
B. R. McDonald 1
Robert R. Burnside 1
S.R. Butcher 1
Konrad J. Heuvers 1
Richard Rasala 1
Bernard R. McDonald 1
Stephen U. Chase 1
S.L. Ma 1
Wolfgang Schwarz 1
Hee Jung Lee 1
J. S. Milne 1
Donald G. James 1
Angelo J. Christino 1
Commonly Cited References
Action Title Year Authors # of times referenced
+ Introduction to Affine Group Schemes 1979 William C. Waterhouse
 15
+ Pairs of quadratic forms 1976 William C. Waterhouse
 8
+ Formal Complex Multiplication in Local Fields 1965 Jonathan Lubin
John Tate
 4
+ Invertibility of linear maps preserving matrix invariants 1983 William C. Waterhouse
 3
+ PDF Chat Linear Transformations on Algebras of Matrices: The Invariance of the Elementary Symmetric Functions 1959 Marvin Marcus
Roger Purves
 3
+ The equivalence of bilinear forms 1974 Carl Riehm
 3
+ PDF Chat Hopf Algebras and Galois Theory 1969 Stephen U. Chase
Moss E. Sweedler
 3
+ When Hopf algebras are Frobenius algebras 1971 Bodo Pareigis
 3
+ A theory of linear descent based upon Hopf algebraic techniques 1969 Harry P Allen
Moss E. Sweedler
 3
+ Structure groups and Lie algebras of Jordan algebras of symmetric elements of associative algebras with involution 1976 Nathan Jacobson
 3
+ Finite Subgroups and Isogenies of One-Parameter Formal Lie Groups 1967 Jonathan Lubin
 3
+ 𝑅-linear endomorphisms of (𝑅)_{𝑛} preserving invariants 1983 Bernard R. McDonald
 3
+ PDF Chat Pairs of symmetric bilinear forms in characteristic 2 1977 William C. Waterhouse
 3
+ PDF Chat Roots and canonical forms for circulant matrices 1963 C. M. Ablow
J. L. Brenner
 3
+ PDF Chat Linear Transformations on Matrices: the Invariance of the Third Elementary Symmetric Function 1970 LeRoy B. Beasley
 3
+ A Units Theorem Applied to Hopf Algebras and Amitsur Cohomology 1970 Moss E. Sweedler
 3
+ Automorphisms of det(Xij): The group scheme approach 1987 William C. Waterhouse
 3
+ Abelian l-Adic Representations and Elliptic Curves 1997 Jean-Pierre Serre
 3
+ Introduction to Quadratic Forms 1973 O. T. O’Meara
 3
+ Trace preserving linear transformations on matrix algebras 1977 Amos Kovascs
 3
+ Projectivities over rings with many units 1981 Bernard R. McDonald
 3
+ PDF Chat Commutative group schemes 1966 Frans J. Oort
 3
+ One-Parameter Formal Lie Groups Over -Adic Integer Rings 1964 Jonathan Lubin
 3
+ Éléments de géométrie algébrique 1964 Alexandre Grothendieck
 2
+ Linear transformations of the second elementary function 1981 Donald G. James
 2
+ Clifford Algebras and Spinor Norms Over a Commutative Ring 1974 Hyman Bass
 2
+ PDF Chat On the formal group laws of unoriented and complex cobordism theory 1969 Daniel Quillen
 2
+ Algebras over zero-dimensional rings 1976 K. R. Goodearl
Robert B. Warfield
 2
+ Quadratic spaces with trivial art invariant 1985 M. A. Knus
Antonio Paques
 2
+ PDF Chat An introduction to the theory of numbers 1960 G. H. Hardy
 2
+ The algebraic structure and deformation of pfaffian schemes 1980 H. Kleppe
Dan Laksov
 2
+ Finite dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple 1988 Richard G. Larson
David E. Radford
 2
+ PDF Chat On Fermat varieties 1979 Tetsuji Shioda
Toshiyuki Katsura
 2
+ One-dimensional affine group schemes 1980 William C. Waterhouse
Boris Weisfeiler
 2
+ Hermitesche und orthogonale Operatoren �ber kommutativen Ringen 1973 F. Ischebeck
Winfried Scharlau
 2
+ Gl<sub>2</sub>of rings with many units 1980 Bernard R. McDonald
 2
+ On the Jacobian variety of the Fermat curve 1980 Noriko Yui
 2
+ Representations of Algebraic Groups 2007 Jens Carsten Jantzen
 2
+ Linear algebraic groups 1966 Armand Borel
 2
+ Linear maps preserving reduced norms 1982 William C. Waterhouse
 2
+ PDF Chat On linear algebraic semigroups 1980 Mohan S. Putcha
 2
+ PDF Chat Faisceaux amples sur les schémas en groupes et les espaces homogènes 1970 Michel Raynaud
 2
+ Linear Algebraic Groups 1975 James E. Humphreys
 2
+ Self-adjoint operators and formally real fields 1976 William C. Waterhouse
 2
+ Classes of restricted Lie algebras of characteristic p, II 1943 Nathan Jacobson
 2
+ Aut(GL<sub>2</sub>(R)) for rings with many units 1981 Bernard R. McDonald
 2
+ PDF Chat Automorphisms of 𝐺𝐿_{𝑛}(𝑅) 1976 Bernard R. McDonald
 2
+ Discriminant preserving linear maps 1979 Stephen Piercet
 2
+ Le Journal mathématique de Gauss. Traduction française annotée 1956 Paul Eymard
J.P. Lafon
 2
+ UNIPOTENT GROUP SCHEMES OVER INTEGRAL RINGS 1974 B J Veĭsfeĭler
I V Dolgačëv
 2