On complementability of certain generalized hypercenters in Artinian modules
We prove that, in an Artinian module, the upper FC-hypercenter over an infinite FC-hypercentral locally solvable group has a direct complement. Thus, we obtain a generalization of one of Zaitsev’s theorems and one of Duan’s theorems.
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| Date: | 1997 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5154 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511355717550080 |
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| author | Kurdachenko, L. A. Petrenko, B. V. Subbotin, I. Ya. Курдаченко, Л. А. Петренко, Б. В. Суботін, І. Я. |
| author_facet | Kurdachenko, L. A. Petrenko, B. V. Subbotin, I. Ya. Курдаченко, Л. А. Петренко, Б. В. Суботін, І. Я. |
| author_sort | Kurdachenko, L. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:25:50Z |
| description | We prove that, in an Artinian module, the upper FC-hypercenter over an infinite FC-hypercentral locally solvable group has a direct complement. Thus, we obtain a generalization of one of Zaitsev’s theorems and one of Duan’s theorems. |
| first_indexed | 2026-03-24T03:11:35Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5154 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:11:35Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/64/ed72aea599af114d8db2b784422af264.pdf |
| spelling | umjimathkievua-article-51542020-03-18T21:25:50Z On complementability of certain generalized hypercenters in Artinian modules Про доповшованість деяких узагальнених гіперцентрів у артінових модулях Kurdachenko, L. A. Petrenko, B. V. Subbotin, I. Ya. Курдаченко, Л. А. Петренко, Б. В. Суботін, І. Я. We prove that, in an Artinian module, the upper FC-hypercenter over an infinite FC-hypercentral locally solvable group has a direct complement. Thus, we obtain a generalization of one of Zaitsev’s theorems and one of Duan’s theorems. Доведено, що в артіновім модулі над нескінченною em class="a-plus-plus">FC-гіперцентральною локально розв'язною групою верхній FC-гіперцентр має пряме доповнення. Таким чином, отримано узагальнення теорем Д. І. Зайцева і З. Дуана. Institute of Mathematics, NAS of Ukraine 1997-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5154 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 11 (1997); 1548–1552 Український математичний журнал; Том 49 № 11 (1997); 1548–1552 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5154/7004 https://umj.imath.kiev.ua/index.php/umj/article/view/5154/7005 Copyright (c) 1997 Kurdachenko L. A.; Petrenko B. V.; Subbotin I. Ya. |
| spellingShingle | Kurdachenko, L. A. Petrenko, B. V. Subbotin, I. Ya. Курдаченко, Л. А. Петренко, Б. В. Суботін, І. Я. On complementability of certain generalized hypercenters in Artinian modules |
| title | On complementability of certain generalized hypercenters in Artinian modules |
| title_alt | Про доповшованість деяких узагальнених гіперцентрів у артінових модулях |
| title_full | On complementability of certain generalized hypercenters in Artinian modules |
| title_fullStr | On complementability of certain generalized hypercenters in Artinian modules |
| title_full_unstemmed | On complementability of certain generalized hypercenters in Artinian modules |
| title_short | On complementability of certain generalized hypercenters in Artinian modules |
| title_sort | on complementability of certain generalized hypercenters in artinian modules |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5154 |
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