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- Title
On the P.Q.-Baer Skew Generalized Power Series Modules.
- Abstract
For a ring R and a strictly totally ordered monoid (S , ≤) , let ω : 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 , m R b = 0 if and only if m ω (s) (R b) = 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.
- Subjects
POWER series; ENDOMORPHISM rings; IDEMPOTENTS; HOMOMORPHISMS
- Publication
Algebra Colloquium, 2022, Vol 29, Issue 3, p405
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S100538672200030X