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On the P.Q.-Baer Skew Generalized Power Series Modules
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作者 ali majidinya 《Algebra Colloquium》 SCIE CSCD 2022年第3期405-418,共14页
For a ring R and a strictly totally ordered monoid(S,≤),letω:S→End(R)be a monoid homomorphism and M an(S,ω)-weakly rigid right R-module(i.e.,for any elements m∈M,b∈R and s∈S,mRb=0 if and only if mω(s)(Rb)=0),w... For a ring R and a strictly totally ordered monoid(S,≤),letω:S→End(R)be a monoid homomorphism and M an(S,ω)-weakly rigid right R-module(i.e.,for any elements m∈M,b∈R and s∈S,mRb=0 if and only if mω(s)(Rb)=0),where End(R)is the ring of ring endomorphisms of R.It is shown that the skew generalized power series module M[[S]]_(R[[S,ω]])is a principally quasi-Baer module if and only if the annihilator of every submodule generated by an S-indexed subset of M is generated by an idempotent as a right ideal of R.As a consequence we deduce that for an(S,ω)-weakly rigid ring R,the skew generalized power series ring R[[S,ω]]is right principally quasi-Baer if and only if R is right principally quasi-Baer and any S-indexed subset of right semicentral idempotents in R has a generalized S-indexed join in R.The range of previous results in this area is expanded by these results. 展开更多
关键词 module of skew generalized power series strictly ordered monoid principally quasi-Baerring weaklyrigidmodule
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