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Relative natural classes and relative injectivity
Let Ï„ 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 Ï„-natural class as a class of modules closed under Ï„-dense submodules, direct sums, and Ï„-injective hulls. We study connections between certain conditions involving Ï„-(quasi-)injectivity in the context of Ï„-natural classes, generalizing results established by S. S. Page and Y. Q. Zhou
(1994) for natural classes