On the P.Q.-Baer Skew Generalized Power Series Modules

作     者：Ali Majidinya 

作者机构：Department of Mathematical SciencesSalman Farsi University of Kazerun KazerunP.O.Box 73175-457Iran 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2022年第29卷第3期

页      面：405-418页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：module of skew generalized power series strictly ordered monoid principally quasi-Baerring weaklyrigidmodule 

摘      要：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 *** 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 *** 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 *** range of previous results in this area is expanded by these results.