On torsionfree classes which are not precover classes

Ladislav Bican

Displaying similar documents to “On torsionfree classes which are not precover classes”

Cotorsion modules for torsion theories

Henderson, J., Orzech, M. (1977)

Portugaliae mathematica

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Rings admitting torsion injective covers

Ahsan, J., Enochs, E. (1981)

Portugaliae mathematica

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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...

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...