Density relative to a torsion theory

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Ranks of modules relative to a torsion theory

Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and c...

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ranks of modules relative to a torsion theory

relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $m$, called {em $tau$-rank of} $m$, which coincides with the reduced rank of $m$ whenever $tau$ is the goldie torsion theory. it is shown that the $tau$-rank of $m$ is measured by the length of certain decompositions of the $tau$-injective hull of $m$. moreover, some relations between the $tau$-rank of $m$ and c...

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–supplemented Modules Relative to a Torsion Theory

Let R be ring and M a right R-module. This article introduces the concept of τ −⊕-supplemented modules as follows: Given a hereditary torsion theory in Mod-R with associated torsion functor τ we say that a module M is τ −⊕-supplemented when for every submodule N of M there exists a direct summand K of M such that M = N +K and N ∩K is τ−torsion, and M is called completely τ −⊕-supplemented if ev...

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A relative extending module and torsion precovers

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a relative extending module and torsion precovers

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ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 1981

ISSN: 0002-9939

DOI: 10.1090/s0002-9939-1981-0614872-7