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...

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 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...