International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 5, Pages 671-678
doi:10.1155/IJMMS.2005.671

Relative natural classes and relative injectivity.

Abstract

Let τ be a hereditary torsion theory on the category R-Mod of left R-modules over an associative unitary ring R. We introduce the notion of τ-natural class as a class of modules closed under τ-dense submodules, direct sums, and τ-injective hulls. We study connections between certain conditions involving τ-(quasi-)injectivity in the context of τ-natural classes, generalizing results established by S. S. Page and Y. Q. Zhou (1994) for natural classes.