On Finitely Annihilated Modules

Abstract

Let R be a commutative ring with identity and M be a unitary R-module. An R-module M is called finitely annihilated if there exists a finitely generated R-submodule N of M such that ann(M)=ann(N).Our main purpose in this work is to study this property in some known classes of modules such as quasi-injective, multiplication and other modules. We prove that: 1-If M is a quasi-injective R-module, then M is finitely annihilated if and only if M is finendo. 2-If M is a multiplication R-module, then M is finitely annihilated if and only if M is finitely generated. 3-M is a faithful finitely annihilated R-module if and only if M is a compactly faithful R-module.