On generalized morphic modules

Abstract 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.