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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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.671 |
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| _version_ | 1832549486708129792 |
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| author | Septimiu Crivei |
| author_facet | Septimiu Crivei |
| author_sort | Septimiu Crivei |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-05f321079d2e473cb9a3386bcbf49509 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-05f321079d2e473cb9a3386bcbf495092025-02-03T06:11:08ZengWileyInternational 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 |
| spellingShingle | Septimiu Crivei Relative natural classes and relative injectivity International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | Relative natural classes and relative injectivity |
| title_sort | relative natural classes and relative injectivity |
| url | http://dx.doi.org/10.1155/IJMMS.2005.671 |
| work_keys_str_mv | AT septimiucrivei relativenaturalclassesandrelativeinjectivity |