Displaying similar documents to “ f -derivations on rings and modules”

Extending modules relative to a torsion theory

Semra Doğruöz (2008)

Czechoslovak Mathematical Journal

Similarity:

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...

Precovers and Goldie’s torsion theory

Ladislav Bican (2003)

Mathematica Bohemica

Similarity:

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...