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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 5, Pages 671-678

Relative natural classes and relative injectivity

Department of Mathematics, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 Mihail Kogălniceanu Street, Cluj-Napoca 400084, Romania

Received 20 October 2004; Revised 24 January 2005

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.