Displaying similar documents to “On generalized q.f.d. modules”

Countably thick modules

Ali Abdel-Mohsen, Mohammad Saleh (2005)

Archivum Mathematicum

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The purpose of this paper is to further the study of countably thick modules via weak injectivity. Among others, for some classes ℳ of modules in σ [ M ] we study when direct sums of modules from ℳ satisfies a property ℙ in σ [ M ] . In particular, we get characterization of locally countably thick modules, a generalization of locally q.f.d. modules.

On weakly projective and weakly injective modules

Mohammad Saleh (2004)

Commentationes Mathematicae Universitatis Carolinae

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The purpose of this paper is to further the study of weakly injective and weakly projective modules as a generalization of injective and projective modules. For a locally q.f.d. module M , there exists a module K ∈ σ [ M ] such that K ⊕ N is weakly injective in σ [ M ] , for any N ∈ σ [ M ] . Similarly, if M is projective and right perfect in σ [ M ] , then there exists a module K ∈ σ [ M ] such that K ⊕ N is weakly projective in σ [ M ] , for any N ∈ σ [ M ] . Consequently, over a right perfect ring every module is a direct summand of a weakly projective...

On μ -singular and μ -extending modules

Yahya Talebi, Ali Reza Moniri Hamzekolaee (2012)

Archivum Mathematicum

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Let M be a module and μ be a class of modules in Mod - R which is closed under isomorphisms and submodules. As a generalization of essential submodules Özcan in [8] defines a μ -essential submodule provided it has a non-zero intersection with any non-zero submodule in μ . We define and investigate μ -singular modules. We also introduce μ -extending and weakly μ -extending modules and mainly study weakly μ -extending modules. We give some characterizations of μ -co-H-rings by weakly μ -extending modules....

A generalization of the finiteness problem of the local cohomology modules

Ahmad Abbasi, Hajar Roshan-Shekalgourabi (2014)

Czechoslovak Mathematical Journal

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Let R be a commutative Noetherian ring and 𝔞 an ideal of R . We introduce the concept of 𝔞 -weakly Laskerian R -modules, and we show that if M is an 𝔞 -weakly Laskerian R -module and s is a non-negative integer such that Ext R j ( R / 𝔞 , H 𝔞 i ( M ) ) is 𝔞 -weakly Laskerian for all i < s and all j , then for any 𝔞 -weakly Laskerian submodule X of H 𝔞 s ( M ) , the R -module Hom R ( R / 𝔞 , H 𝔞 s ( M ) / X ) is 𝔞 -weakly Laskerian. In particular, the set of associated primes of H 𝔞 s ( M ) / X is finite. As a consequence, it follows that if M is a finitely generated R -module and N is...