$I$-Radicals, Their Lattices, and Some Classes of Rings
We describe some I-radicals in the categories of modules over semilocal rings. We give a characterization of rings over which the set of I-radicals coincides with the set of hereditary idempotent radicals. We prove that the lattices of I-radicals in the categories of modules over Morita-equivalent r...
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| Date: | 2002 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4141 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510275125379072 |
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| author | Gorbachuk, E. L. Maturin, Yu. P. Горбачук, О. Л. Матурін, Ю. П. |
| author_facet | Gorbachuk, E. L. Maturin, Yu. P. Горбачук, О. Л. Матурін, Ю. П. |
| author_sort | Gorbachuk, E. L. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:23:13Z |
| description | We describe some I-radicals in the categories of modules over semilocal rings. We give a characterization of rings over which the set of I-radicals coincides with the set of hereditary idempotent radicals. We prove that the lattices of I-radicals in the categories of modules over Morita-equivalent rings are isomorphic. |
| first_indexed | 2026-03-24T02:54:24Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4141 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:54:24Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/81/7fb6cfcf8af18107e27516e9b3ebb381.pdf |
| spelling | umjimathkievua-article-41412020-03-18T20:23:13Z $I$-Radicals, Their Lattices, and Some Classes of Rings $I$-Радикали, їх ґратки і деякі класи кілець Gorbachuk, E. L. Maturin, Yu. P. Горбачук, О. Л. Матурін, Ю. П. We describe some I-radicals in the categories of modules over semilocal rings. We give a characterization of rings over which the set of I-radicals coincides with the set of hereditary idempotent radicals. We prove that the lattices of I-radicals in the categories of modules over Morita-equivalent rings are isomorphic. Описуються деякі $I$-радикали в категоріях модулів над напівлокальними кільцями. Наведено харакгеризацію кілець, над якими множина $I$ радикалів збігається з множиною скрутів. Доводиться, що ґратки $I$ радикалів у категоріях модулів над Моріта-еквівалешними кільцями є ізоморфними. Institute of Mathematics, NAS of Ukraine 2002-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4141 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 7 (2002); 1016-1019 Український математичний журнал; Том 54 № 7 (2002); 1016-1019 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/4141/4991 https://umj.imath.kiev.ua/index.php/umj/article/view/4141/4992 Copyright (c) 2002 Gorbachuk E. L.; Maturin Yu. P. |
| spellingShingle | Gorbachuk, E. L. Maturin, Yu. P. Горбачук, О. Л. Матурін, Ю. П. $I$-Radicals, Their Lattices, and Some Classes of Rings |
| title | $I$-Radicals, Their Lattices, and Some Classes of Rings |
| title_alt | $I$-Радикали, їх ґратки і деякі класи кілець |
| title_full | $I$-Radicals, Their Lattices, and Some Classes of Rings |
| title_fullStr | $I$-Radicals, Their Lattices, and Some Classes of Rings |
| title_full_unstemmed | $I$-Radicals, Their Lattices, and Some Classes of Rings |
| title_short | $I$-Radicals, Their Lattices, and Some Classes of Rings |
| title_sort | $i$-radicals, their lattices, and some classes of rings |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4141 |
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