Let (𝒯, ℱ) be a hereditary torsion theory for A ℳ, the category of left A-modules. In this paper
the property that the torsionfree class ℱ be closed under homomorphic images is …

Let τ be a hereditary torsion theory. We mention a characterization of τ-quasi-injective
modules, as fully invariant submodules of their τ-injective hull, and we give some properties …

Recently Rim and Teply [11] found a necessary condition for the existence of $\sigma $-
torsionfree covers with respect to a given hereditary torsion theory for the category $ R …

Throughout the paper A will denote an artin algebra and mod A will denote the category of
finitely generated A-modules. Recently, subcategories of mod A which are the torsion free …

Let P be a finitely generated projective right A-module with trace ideal T and A-
endomorphism ring B. Associated with P are the TTF classes, 𝒯 F={⋅ AX∣ P⊗ X= 0} and 𝒯 …

91. Background A subclass T of mod-R is called an hereditary torsion class if it is closed
under submodul es, homomorphic images, extensions and direct sums. The class T …

Let R be an associative ring with 1 and let T be a hereditary torsion theory in the category of
left R-modules. In defining the localizatio n of R respect to x, the concept of T-injective …

For an arbitrary, abstract class L of right R-modules, various characterisations of L-injectivity
are given assuming various natural conditions on L. We investigate what the minimum …

Let (𝒯, ℱ) denote a hereditary torsion theory for the category of modules over a ring R. In this
paper the splitting of projective modules is studied, and it is shown that this is not equivalent …

The purpose of this paper is to introduce the study of perfect torsion theories on
$\operatorname {Mod} R $ and to dualize the concept of divisible module. A torsion theory …