On Baer modules

Chillumuntala Jayaram ^[1] ; Ünsal Tekir ^[2] ; Suat Koç ^[3]
1. [1] The University of West Indies, Barbados
2. [2] Marmara University,Turkey
3. [3] Istanbul Medeniyet University, Turkey
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Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 63, Nº. 1, 2022, págs. 109-128
Idioma: inglés
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Resumen
- Abstract. 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 a previous work by Jayaram and Tekir. Let R be a commutative ring with a nonzero identity and let 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 a certain class of modules/submodules such as von Neumann regular modules/prime submodules in terms of Baer modules.