On extensions of Baer and quasi-Baer modules

Acta Universitatis Sapientiae. Matematica

E. Hashemi¹ 

关键词: S-compatible module;    reduced module;    Baer module;    Quasi-Baer;    module;    skew monoid ring;   

DOI  :  10.2478/ausm-2018-0032

学科分类：社会科学、人文和艺术（综合）

来源: Editura Scientia / Scientia Publishing House

【 摘 要 】

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 ∈ Mand 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]RS is quasi-Baer, (2) MR is Baer (resp. p.p) if and only if M[S]RS 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.

【 授权许可】

Unknown