Revista De La Union Matematica Argentina, cilt.63, ss.1-19, 2022 (SCI-Expanded)
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.