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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.

$(n, d)$ -injective covers, $n$ -coherent rings, and $(n, d)$ -rings

Weiqing Li, Baiyu Ouyang (2014)

Czechoslovak Mathematical Journal

It is known that a ring $R$ is left Noetherian if and only if every left $R$ -module has an injective (pre)cover. We show that $(1)$ if $R$ is a right $n$ -coherent ring, then every right $R$ -module has an $(n, d)$ -injective (pre)cover; $(2)$ if $R$ is a ring such that every $(n, 0)$ -injective right $R$ -module is $n$ -pure extending, and if every right $R$ -module has an $(n, 0)$ -injective cover, then $R$ is right $n$ -coherent. As applications of these results, we give some characterizations of $(n, d)$ -rings, von Neumann regular rings and semisimple rings....

...-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.

...-projektive Moduln.

Wolfgang Zimmermann (1977)

Journal für die reine und angewandte Mathematik

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

Christian Siebeneicher (1976)

Mathematische Zeitschrift

...-semiperfekte und ...-perfekte Moduln.

Robert Wisbauer (1978)

Mathematische Zeitschrift

$Δ$ -endomorphism near-rings.

Dasić, Vucić (1980)

Publications de l'Institut Mathématique. Nouvelle Série

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

Wang, Yongduo (2007)

International Journal of Mathematics and Mathematical Sciences

$λ$ -чистота модулей над кольцом дискретных нормированний.

А.П. Ераскина (1973)

Sibirskij matematiceskij zurnal

$σ$ -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...

$ω_{1}$ -generated uniserial modules over chain rings

Jan Žemlička (2004)

Commentationes Mathematicae Universitatis Carolinae

The purpose of this paper is to provide a criterion of an occurrence of uncountably generated uniserial modules over chain rings. As we show it suffices to investigate two extreme cases, nearly simple chain rings, i.e. chain rings containing only three two-sided ideals, and chain rings with “many” two-sided ideals. We prove that there exists an $ω_{1}$ -generated uniserial module over every non-artinian nearly simple chain ring and over chain rings containing an uncountable strictly increasing (resp. decreasing)...

Currently displaying 1 – 20 of 172

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Displaying 1 – 20 of 172

$\oplus$ -cofinitely supplemented modules

$⋂$ -compact modules

$(n, d)$ -injective covers, $n$ -coherent rings, and $(n, d)$ -rings

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

*-multilinear polynomials with invertible values

ℵ-products of modules and splitness.

...-projektive Moduln.

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

...-semiperfekte und ...-perfekte Moduln.

$Δ$ -endomorphism near-rings.

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

$λ$ -чистота модулей над кольцом дискретных нормированний.

$σ$ -semisimple rings.

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

$ω_{1}$ -generated uniserial modules over chain rings

Алгебраически компактные модули и относительная гомологическая алгебра над ручными наследственными алгебрами.

Алгебраические автоморфизмы и PI-алгебры

Алгебры, заданные двумя квадратичными соотношениями

Алгебры и полугруппы с квадратичными функциями роста

Алгебры Хопфа с инволюцией над некоммутативными кольцами и их гомологии. I

Currently displaying 1 – 20 of 172