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-cofinitely supplemented modules

H. Çalışıcı, A. Pancar (2004)

Czechoslovak Mathematical Journal

Let R be a ring and M a right R -module. M is called -cofinitely supplemented if every submodule N of M with M N finitely generated has a supplement that is a direct summand of M . In this paper various properties of the -cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of -cofinitely supplemented modules is -cofinitely supplemented. (2) A ring R is semiperfect if and only if every free R -module is -cofinitely supplemented. In addition, if M has the summand sum...

-compact modules

Tomáš Kepka (1995)

Commentationes Mathematicae Universitatis Carolinae

The duals of -compact modules are briefly discussed.

A generalization of Mathieu subspaces to modules of associative algebras

Wenhua Zhao (2010)

Open Mathematics

We first propose a generalization of the notion of Mathieu subspaces of associative algebras 𝒜 , which was introduced recently in [Zhao W., Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl. Algebra, 2010, 214(7), 1200–1216] and [Zhao W., Mathieu subspaces of associative algebras], to 𝒜 -modules . The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion, we also introduce the sets σ(N) and τ(N) of stable...

A note on V-rings

Andreas G. Athanasiadis (1971)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Add ( U ) of a uniserial module

Pavel Příhoda (2006)

Commentationes Mathematicae Universitatis Carolinae

A module is called uniserial if it has totally ordered submodules in inclusion. We describe direct summands of U ( I ) for a uniserial module U . It appears that any such a summand is isomorphic to a direct sum of copies of at most two uniserial modules.

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