Regularly weakly based modules over right perfect rings and Dedekind domains

Michal Hrbek; Pavel Růžička

Displaying similar documents to “Regularly weakly based modules over right perfect rings and Dedekind domains”

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 $K \in σ [M]$ such that $K \oplus N$ is weakly injective in $σ [M]$ , for any $N \in σ [M]$ . Similarly, if $M$ is projective and right perfect in $σ [M]$ , then there exists a module $K \in σ [M]$ such that $K \oplus N$ is weakly projective in $σ [M]$ , for any $N \in σ [M]$ . 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...

Weak multiplication modules over a pullback of Dedekind domains

S. Ebrahimi Atani, F. Farzalipour (2009)

Colloquium Mathematicae

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Let R be the pullback, in the sense of Levy [J. Algebra 71 (1981)], of two local Dedekind domains. We classify all those indecomposable weak multiplication R-modules M with finite-dimensional top, that is, such that M/Rad(R)M is finite-dimensional over R/Rad(R). We also establish a connection between the weak multiplication modules and the pure-injective modules over such domains.