<abstract xmlns="http://www.w3.org/1999/xhtml">Let R be a ring, MR a module, S a monoid, ω : S → End(R) a monoid homomorphism and R * S a skew monoid ring. Then M[S] = {m1g1 + · · · + mngn | n ≥ 1, mi ∈ M and gi ∈ S for each 1 ≤ i ≤ n} is a module over R ∗ S. A module MR is <italic>Baer</italic> (resp. <italic>quasi-Baer</italic>) if the annihilator of every subset (resp. submodule) of M is generated by an idempotent of R. In this paper we impose S-compatibility assumption on the module MR and prove: (1) MR is quasi-Baer if and only if M[s]R∗S is quasi-Baer, (2) MR is Baer (resp. p.p) if and only if M[S]R∗S is Baer (resp. p.p), where MR is S-skew Armendariz, (3) MR satisfies the ascending chain condition on annihilator of submodules if and only if so does M[S]R∗S, where MR is S-skew quasi-Armendariz.</abstract>

Let R be a ring, MR a module, S a monoid, ω : S → End(R) a monoid homomorphism and R * S a skew monoid ring. Then M[S] = {m1g1 + · · · + mngn | n ≥ 1, mi ∈ M and gi ∈ S for each 1 ≤ i ≤ n} is a module over R ∗ S. A module MR is Baer (resp. quasi-Baer) if the annihilator of every subset (resp. submodule) of M is generated by an idempotent of R. In this paper we impose S-compatibility assumption on the module MR and prove: (1) MR is quasi-Baer if and only if M[s]R∗S is quasi-Baer, (2) MR is Baer (resp. p.p) if and only if M[S]R∗S is Baer (resp. p.p), where MR is S-skew Armendariz, (3) MR satisfies the ascending chain condition on annihilator of submodules if and only if so does M[S]R∗S, where MR is S-skew quasi-Armendariz.

On extensions of Baer and quasi-Baer modules

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On extensions of Baer and quasi-Baer modules"}

Let R be a ring, MR a module, S a monoid, ω : S → End(R) a monoid homomorphism and R * S a skew monoid ring. Then M[S] = {m1g1 + · · · + mngn | n ≥ 1, mi ∈ M...

On extensions of Baer and quasi-Baer modules

Published Online: Mar 04, 2019

Page range: 402 - 417

Received: Jun 12, 2018

DOI: https://doi.org/10.2478/ausm-2018-0032

Keywords
S-compatible module, reduced module, Baer module, Quasi-Baer module, skew monoid ring

© 2018 Ebrahim Hashemi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On extensions of Baer and quasi-Baer modules

Published Online: Mar 04, 2019

Page range: 402 - 417

Received: Jun 12, 2018

DOI: https://doi.org/10.2478/ausm-2018-0032

KeywordsS-compatible module, reduced module, Baer module, Quasi-Baer module, skew monoid ring

© 2018 Ebrahim Hashemi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
S-compatible module, reduced module, Baer module, Quasi-Baer module, skew monoid ring