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

Methods of calculating cohomological and Hochschild-Mitchell dimensions of finite partially ordered sets.

Husainov, A.A.; Pancar, A. — 2001

Homology, Homotopy and Applications

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⊕ -cofinitely supplemented modules

Methods of calculating cohomological and Hochschild-Mitchell dimensions of finite partially ordered sets.

$\oplus$ -cofinitely supplemented modules