Type: Article
Publication Date: 2011-04-12
Citations: 7
DOI: https://doi.org/10.1142/s0219498811005014
A ring R is called a left APP-ring if the left annihilator l R (Ra) is right s-unital as an ideal of R for any a ∈ R. Let R be a ring, (S, ≤) be a commutative strictly ordered monoid and ω: S → End (R) be a monoid homomorphism. The skew generalized power series ring [[R S, ≤ , ω]] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings and Malcev–Neumann Laurent series rings. We study the left APP-property of the skew generalized power series ring [[R S, ≤ , ω]]. It is shown that if (S, ≤) is a commutative strictly totally ordered monoid, ω: S→ Aut (R) a monoid homomorphism and R a ring satisfying the descending chain condition on right annihilators, then [[R S, ≤ , ω]] is left APP if and only if for any S-indexed subset A of R, the ideal l R (∑ a ∈ A ∑ s ∈ S Rω s (a)) is right s-unital.