On weakly projective and weakly injective modules

Mohammad Saleh

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 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...

Displaying similar documents to “On weakly projective and weakly injective modules”

Countably thick modules

On generalized q.f.d. modules