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 annR (m) = (a) + annR (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.

Keywords

• baer ring
• generalized morphic ring
• baer module
• weak quasi regular module
• generalized morphic module
• primary 16e50, 13a15