Precovers and Goldie’s torsion theory

Ladislav Bican

Displaying similar documents to “Precovers and Goldie’s torsion theory”

Relatively exact modules

Ladislav Bican (2003)

Commentationes Mathematicae Universitatis Carolinae

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Rim and Teply [10] investigated relatively exact modules in connection with the existence of torsionfree covers. In this note we shall study some properties of the lattice $ℰ_{τ} (M)$ of submodules of a torsionfree module $M$ consisting of all submodules $N$ of $M$ such that $M / N$ is torsionfree and such that every torsionfree homomorphic image of the relative injective hull of $M / N$ is relatively injective. The results obtained are applied to the study of relatively exact covers of torsionfree modules. As...

Extending modules relative to a torsion theory

Semra Doğruöz (2008)

Czechoslovak Mathematical Journal

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An $R$ -module $M$ is said to be an extending module if every closed submodule of $M$ is a direct summand. In this paper we introduce and investigate the concept of a type 2 $τ$ -extending module, where $τ$ is a hereditary torsion theory on $Mod$ - $R$ . An $R$ -module $M$ is called type 2 $τ$ -extending if every type 2 $τ$ -closed submodule of $M$ is a direct summand of $M$ . If $τ_{I}$ is the torsion theory on $Mod$ - $R$ corresponding to an idempotent ideal $I$ of $R$ and $M$ is a type 2 $τ_{I}$ -extending $R$ -module, then the question of whether...

Relative exact covers

Ladislav Bican, Blas Torrecillas (2001)

Commentationes Mathematicae Universitatis Carolinae

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Recently Rim and Teply [11] found a necessary condition for the existence of $σ$ -torsionfree covers with respect to a given hereditary torsion theory for the category $R$ -mod. This condition uses the class of $σ$ -exact modules; i.e. the $σ$ -torsionfree modules for which every its $σ$ -torsionfree homomorphic image is $σ$ -injective. In this note we shall show that the existence of $σ$ -torsionfree covers implies the existence of $σ$ -exact covers, and we shall investigate some sufficient conditions for...