On direct decompositions in modules over group rings
In the theory of infinite groups, one of the most important useful generalizations of the classical Maschke theorem is the Kovačs-Newman theorem, which establishes sufficient conditions for the existence of G-invariant complements in modules over a periodic group G finite over the center. We genrali...
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| Date: | 1997 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5002 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511195642986496 |
|---|---|
| author | Petrenko, B. V. Петренко, Б. В. |
| author_facet | Petrenko, B. V. Петренко, Б. В. |
| author_sort | Petrenko, B. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:22:31Z |
| description | In the theory of infinite groups, one of the most important useful generalizations of the classical Maschke theorem is the Kovačs-Newman theorem, which establishes sufficient conditions for the existence of G-invariant complements in modules over a periodic group G finite over the center. We genralize the Kovačs-Newman theorem to the case of modules over a group ring KG, where K is a Dedekind domain. |
| first_indexed | 2026-03-24T03:09:02Z |
| format | Article |
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| id | umjimathkievua-article-5002 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:09:02Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/54/add12241053153e612bd09c61045ec54.pdf |
| spelling | umjimathkievua-article-50022020-03-18T21:22:31Z On direct decompositions in modules over group rings Про прямі розклади у модулях над груповими кільцями Petrenko, B. V. Петренко, Б. В. In the theory of infinite groups, one of the most important useful generalizations of the classical Maschke theorem is the Kovačs-Newman theorem, which establishes sufficient conditions for the existence of G-invariant complements in modules over a periodic group G finite over the center. We genralize the Kovačs-Newman theorem to the case of modules over a group ring KG, where K is a Dedekind domain. В теорії нескінченних груп серед корисних узагальнень класичної теореми Машке досить важливе місце посідає теорема Ковача - Ныомепа, яка дає достатні умови існування G-іііваріаитиих доповнень у модулях над періодичною скінченного над центром групою G. У даній статгі теорему Ковача - Ныомена узагальнено па модулі над груповим кільцем KG, де K дедекіндова область. Institute of Mathematics, NAS of Ukraine 1997-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5002 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 2 (1997); 255–261 Український математичний журнал; Том 49 № 2 (1997); 255–261 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5002/6703 https://umj.imath.kiev.ua/index.php/umj/article/view/5002/6704 Copyright (c) 1997 Petrenko B. V. |
| spellingShingle | Petrenko, B. V. Петренко, Б. В. On direct decompositions in modules over group rings |
| title | On direct decompositions in modules over group rings |
| title_alt | Про прямі розклади у модулях над груповими кільцями |
| title_full | On direct decompositions in modules over group rings |
| title_fullStr | On direct decompositions in modules over group rings |
| title_full_unstemmed | On direct decompositions in modules over group rings |
| title_short | On direct decompositions in modules over group rings |
| title_sort | on direct decompositions in modules over group rings |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5002 |
| work_keys_str_mv | AT petrenkobv ondirectdecompositionsinmodulesovergrouprings AT petrenkobv ondirectdecompositionsinmodulesovergrouprings AT petrenkobv proprâmírozkladiumodulâhnadgrupovimikílʹcâmi AT petrenkobv proprâmírozkladiumodulâhnadgrupovimikílʹcâmi |