Displaying similar documents to “Countably thick 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 generalized q.f.d. modules

Mohammad Saleh, S. K. Jain, Sergio R. López-Permouth (2005)

Archivum Mathematicum

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A right R -module M is called a generalized q.f.d. module if every M-singular quotient has finitely generated socle. In this note we give several characterizations to this class of modules by means of weak injectivity, tightness, and weak tightness that generalizes the results in [sanh1], Theorem 3. In particular, it is shown that a module M is g.q.f.d. iff every direct sum of M -singular M -injective modules in σ [ M ] is weakly injective iff every direct sum of M -singular weakly tight is weakly...

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...