Relative natural classes and relative injectivity

Relative natural classes and relative injectivity

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 invol...

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Main Author: Septimiu Crivei
Format: Article
Language:English
Published: Hindawi Limited 2005-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/IJMMS.2005.671
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spelling doaj-05f321079d2e473cb9a3386bcbf495092020-11-24T23:59:50ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005567167810.1155/IJMMS.2005.671Relative natural classes and relative injectivitySeptimiu Crivei0Department of Mathematics, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 Mihail Kogălniceanu Street, Cluj-Napoca 400084, RomaniaLet 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.http://dx.doi.org/10.1155/IJMMS.2005.671
collection DOAJ
language English
format Article
sources DOAJ
author Septimiu Crivei
spellingShingle Septimiu Crivei
Relative natural classes and relative injectivity
International Journal of Mathematics and Mathematical Sciences
author_facet Septimiu Crivei
author_sort Septimiu Crivei
title Relative natural classes and relative injectivity
title_short Relative natural classes and relative injectivity
title_full Relative natural classes and relative injectivity
title_fullStr Relative natural classes and relative injectivity
title_full_unstemmed Relative natural classes and relative injectivity
title_sort relative natural classes and relative injectivity
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2005-01-01
description 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.
url http://dx.doi.org/10.1155/IJMMS.2005.671
work_keys_str_mv AT septimiucrivei relativenaturalclassesandrelativeinjectivity
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