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 of modules in we study when direct sums of modules from satisfies a property in . In particular, we get characterization of locally countably thick modules, a generalization of locally q.f.d. modules.
Mohammad Saleh, S. K. Jain, Sergio R. López-Permouth (2005)
Archivum Mathematicum
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A right -module 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 is g.q.f.d. iff every direct sum of -singular -injective modules in is weakly injective iff every direct sum of -singular weakly tight is weakly...
Yahya Talebi, Ali Reza Moniri Hamzekolaee (2012)
Archivum Mathematicum
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Let be a module and be a class of modules in which is closed under isomorphisms and submodules. As a generalization of essential submodules Özcan in [8] defines a -essential submodule provided it has a non-zero intersection with any non-zero submodule in . We define and investigate -singular modules. We also introduce -extending and weakly -extending modules and mainly study weakly -extending modules. We give some characterizations of -co-H-rings by weakly -extending modules....