On Noetherian Modules over Minimax Abelian Groups
We consider modules over minimax Abelian groups. We prove that if A is an Abelian minimax subgroup of the multiplicative group of a field k and if the subring K of the field k generated by the subgroup A is Noetherian, then the subgroup A is the direct product of a periodic group and a finitely gene...
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| Datum: | 2002 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4133 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510268258254848 |
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| author | Tushev, A. V. Тушев, А. В. Тушев, А. В. |
| author_facet | Tushev, A. V. Тушев, А. В. Тушев, А. В. |
| author_sort | Tushev, A. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:23:13Z |
| description | We consider modules over minimax Abelian groups. We prove that if A is an Abelian minimax subgroup of the multiplicative group of a field k and if the subring K of the field k generated by the subgroup A is Noetherian, then the subgroup A is the direct product of a periodic group and a finitely generated group. |
| first_indexed | 2026-03-24T02:54:18Z |
| format | Article |
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| id | umjimathkievua-article-4133 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:54:18Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d7/38f434c20dbbcb5d38641f8d408c56d7.pdf |
| spelling | umjimathkievua-article-41332020-03-18T20:23:13Z On Noetherian Modules over Minimax Abelian Groups О нетеровых модулях над минимаксными абелевыми группами Tushev, A. V. Тушев, А. В. Тушев, А. В. We consider modules over minimax Abelian groups. We prove that if A is an Abelian minimax subgroup of the multiplicative group of a field k and if the subring K of the field k generated by the subgroup A is Noetherian, then the subgroup A is the direct product of a periodic group and a finitely generated group. Вивчаються модулі над мінімаксними абелевими групами. Доведено, що якщо $A$ — абелева мінімаксна підгрупа мультиплікативної групи поля $k$ і підкільце $K$ поля $k$, породжене підгрупою $A$ , ньотерове, то підгрупа $A$ є прямим добутком періодичної та скінченнопородженої групи. Institute of Mathematics, NAS of Ukraine 2002-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4133 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 7 (2002); 969-980 Український математичний журнал; Том 54 № 7 (2002); 969-980 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4133/4975 https://umj.imath.kiev.ua/index.php/umj/article/view/4133/4976 Copyright (c) 2002 Tushev A. V. |
| spellingShingle | Tushev, A. V. Тушев, А. В. Тушев, А. В. On Noetherian Modules over Minimax Abelian Groups |
| title | On Noetherian Modules over Minimax Abelian Groups |
| title_alt | О нетеровых модулях над минимаксными абелевыми группами |
| title_full | On Noetherian Modules over Minimax Abelian Groups |
| title_fullStr | On Noetherian Modules over Minimax Abelian Groups |
| title_full_unstemmed | On Noetherian Modules over Minimax Abelian Groups |
| title_short | On Noetherian Modules over Minimax Abelian Groups |
| title_sort | on noetherian modules over minimax abelian groups |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4133 |
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