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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...

$⋂$ -compact modules

Tomáš Kepka (1995)

Commentationes Mathematicae Universitatis Carolinae

The duals of $\cup$ -compact modules are briefly discussed.

...-Compactness of Reuced Products and Filter Quotients.

A. Laradji (1993)

Manuscripta mathematica

*-multilinear polynomials with invertible values

O. M. Di Vincenzo, A. Valenti (1991)

Rendiconti del Seminario Matematico della Università di Padova

ℵ-products of modules and splitness.

Feng Lianggui (2002)

Publicacions Matemàtiques

Let0 → ∏ℵI Mα ⎯λ→ ∏I Mα ⎯γ→ Coker λ → 0 be an exact sequence of modules, in which ℵ is an infinite cardinal, λ the natural injection and γ the natural surjection. In this paper, the conditions are given mainly in the four theorems so that λ (γ respectively) is split or locally split. Consequently, some known results are generalized. In particular, Theorem 1 of [7] and Theorem 1.6 of [5] are improved.

...-Ringstrukturen auf dem Burnsidering der Permutationsdarstellungen einer endlichen Gruppe.

Christian Siebeneicher (1976)

Mathematische Zeitschrift

$δ$ -small submodules and $δ$ -supplemented modules.

Wang, Yongduo (2007)

International Journal of Mathematics and Mathematical Sciences

$σ$ -semisimple rings.

Boulagouaz, M., Oukhtite, L. (2001)

Beiträge zur Algebra und Geometrie

$τ$ -supplemented modules and $τ$ -weakly supplemented modules

Muhammet Tamer Koşan (2007)

Archivum Mathematicum

Given a hereditary torsion theory $τ = (𝕋, 𝔽)$ in Mod- $R$ , a module $M$ is called $τ$ -supplemented if every submodule $A$ of $M$ contains a direct summand $C$ of $M$ with $A / C$ $τ -$ torsion. A submodule $V$ of $M$ is called $τ$ -supplement of $U$ in $M$ if $U + V = M$ and $U \cap V \leq τ (V)$ and $M$ is $τ$ -weakly supplemented if every submodule...