On Finitely Annihilated Modules
Kirkuk University Journal-Scientific Studies,
2008, Volume 3, Issue 2, Pages 117-133
AbstractLet 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.
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