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In [2], Fuchs and Viljoen introduced and classified the $B^{*}$ -modules for a valuation ring R: an R-module M is a $B^{*}$ -module if $E x t_{R}^{1} (M, X) = 0$ for each divisible module X and each torsion module X with bounded order. The concept of a $B^{*}$ -module was extended to the setting of a torsion theory over an associative ring in [14]. In the present paper, we use categorical methods to investigate the $B^{*}$ -modules for a group graded ring. Our most complete result (Theorem 4.10) characterizes $B^{*}$ -modules for a strongly graded ring R...

Weak incidence algebra and maximal ring of quotients.

Singh, Surjeet, Al-Thukair, Fawzi (2004)

International Journal of Mathematics and Mathematical Sciences

Weak Krull-Schmidt theorem

Ladislav Bican (1998)

Commentationes Mathematicae Universitatis Carolinae

Recently, A. Facchini [3] showed that the classical Krull-Schmidt theorem fails for serial modules of finite Goldie dimension and he proved a weak version of this theorem within this class. In this remark we shall build this theory axiomatically and then we apply the results obtained to a class of some modules that are torsionfree with respect to a given hereditary torsion theory. As a special case we obtain that the weak Krull-Schmidt theorem holds for the class of modules that are both uniform...

When is the category of flat modules abelian?

J. García, J. Martínez Hernández (1995)

Fundamenta Mathematicae

Let Fl(R) denote the category of flat right modules over an associative ring R. We find necessary and sufficient conditions for Fl(R) to be a Grothendieck category, in terms of properties of the ring R.

$τ$ -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...

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The universal skew field of fractions ofa tensor product of free rings

The upper central series of some matrix groups

Tilting sheaves in representation theory of algebras.

Tilting theory - an introduction

Uniform filters

Universal exact sequences for torsion theories

Weak baer modules localized with respect to a torsion theory

Weak Baer modules over graded rings

Weak incidence algebra and maximal ring of quotients.

Weak Krull-Schmidt theorem

When is the category of flat modules abelian?

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

Алгебраические радикалы и радикально-полупростые классы топологических модулей

Двойные локализации и рефлективные подкатегории

Двойственность между локализациями и колокализациями в ситуации сопряженности

Джансовы и идеальные кручения в Морита-контекстах

Дополняемость в решетках кручений. I

Дополняемость в решетках кручений. II

Достаточные условия существования левого кольца частных для кольца, разложенного в прямую сумму левых идеалов

Дуо-кольца, над которыми все кручения являются S-кручениями

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