Precovers

Ladislav Bican; Blas Torrecillas

Displaying similar documents to “Precovers”

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...

Classes of modules related to Serre subcategories.

Crivei, Septimiu, Crivei, Iuliu (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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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...