On Baer modules

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 ann R ( 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.