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 is an element of M, there exists a is an element of R such that ann(R) (m) = (a) + ann(R) (M ), where (a) is the principal ideal generated by an element a is an element of 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.