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Precovers

Ladislav Bican, Blas Torrecillas (2003)

Czechoslovak Mathematical Journal

Let 𝒢 be an abstract class (closed under isomorpic copies) of left R -modules. In the first part of the paper some sufficient conditions under which 𝒢 is a precover class are given. The next section studies the 𝒢 -precovers which are 𝒢 -covers. In the final part the results obtained are applied to the hereditary torsion theories on the category on left R -modules. Especially, several sufficient conditions for the existence of σ -torsionfree and σ -torsionfree σ -injective covers are presented.

Precovers and Goldie’s torsion theory

Ladislav Bican (2003)

Mathematica Bohemica

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 , σ ) is Goldie’s torsion theory and σ is a precover class, then τ is a precover class whenever...

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