On generalized morphic modules

Aim of the present article is to extend generalized morphic ring to modules. Let R be a commutative ring with a unity and M an R-module. M is said to be a generalized morphic module if for each m ∈ M, there exists a ∈ R such that ann_R (m) = (a) + ann_R (M ), where (a) is the principal ideal generated by an element a ∈ R. Many examples and characterizations of generalized morphic modules are given. Moreover, as an application of generalized morphic modules, we use them to characterize Baer modules and principal ideal rings.