2010/05/14 by Renyu Zhao, Zhao, Renyu
Mathematics · #16W60 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16W60
paper · pdf · doi:10.48550/arxiv.1005.2565
10 pages
arxiv created 2010/05/14 · arxiv updated 2010/05/17
A ring R is called a left APP-ring if the left annihilator lR(Ra) is right s-unital as an ideal of R for any a∈ R. Let R be a ring, (S,≤) a strictly ordered monoid and ω:S\longrightarrow \rm End(R) a monoid homomorphism. The skew generalized power series ring [[RS,≤,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 [[RS,≤,ω]]. It is shown that if (S,≤) is a strictly totally ordered monoid, ω:S\longrightarrow \rm Aut(R) a monoid homomorphism and R a ring satisfying descending chain condition on right annihilators, then [[RS,≤,ω]] is left APP if and only if for any S-indexed subset A of R, the ideal lR(∑a∈ A∑s∈ SRωs(a)) is right s-unital.