ON BAER MODULES

Abstract

A commutative ring R is said to be a Baer ring if for each a is an element of R, ann(a) is generated by an idempotent element b E 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 is an element of M there exists a weak idempotent element e is an element of 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.