Extending modules relative to a torsion theory

Semra Doğruöz

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...

Precovers and Goldie’s torsion theory

Ladislav Bican (2003)

Mathematica Bohemica

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Recently, Rim and Teply , using the notion of $τ$ -exact modules, found a necessary condition for the existence of $τ$ -torsionfree covers with respect to a given hereditary torsion theory $τ$ for the category $R$ -mod of all unitary left $R$ -modules over an associative ring $R$ with identity. Some relations between $τ$ -torsionfree and $τ$ -exact covers have been investigated in . The purpose of this note is to show that if $σ = (𝒯_{σ}, ℱ_{σ})$ is Goldie’s torsion theory and $ℱ_{σ}$ is a precover class, then $ℱ_{τ}$ is a precover class...

Displaying similar documents to “Extending modules relative to a torsion theory”

Relatively exact modules

Precovers and Goldie’s torsion theory