On Baer modules
Revista De La Union Matematica Argentina, cilt.63, ss.1-19, 2022 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 63
- Basım Tarihi: 2022
- Doi Numarası: 10.33044/revuma.1741
- Dergi Adı: Revista De La Union Matematica Argentina
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals, DIALNET
- Sayfa Sayıları: ss.1-19
- Marmara Üniversitesi Adresli: Evet
Özet
Recall that a commutative ring R is said to be a Baer ring if
for each a ∈ R, ann(a) is generated by an idempotent element b ∈ R. In
this paper, we extend the notion of a Baer ring to modules in terms of weak
idempotent elements defined in [12]. Let R be a commutative ring with a
nonzero identity and M be a unital R-module. M is said to be a Baer module
if for each m ∈ M, there exists a weak idempotent element e ∈ R such that
annR(m)M = eM. Various examples and properties of Baer modules are
given. Also, we characterize certain class of modules/submodules such as von
Neumann regular modules/prime submodules in terms of Baer modules.