On modules over group rings of soluble groups with commutative ring of scalars
The author studies an \(\bf R\)\(G\)-module \(A\) such that \(\bf R\) is a commutative ring, \(A/C_{A}(G)\) is not a Noetherian \(\bf R\)-module, \(C_{G}(A)=1\), \(G\) is a soluble group. The system of all subgroups \(H \leq G\), for which the quotient modules \(A/C_{A}(H)\) are not Noetherian \(\...
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/650 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543432804139008 |
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| author | Dashkova, O. Yu. |
| author_facet | Dashkova, O. Yu. |
| author_sort | Dashkova, O. Yu. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:17:05Z |
| description | The author studies an \(\bf R\)\(G\)-module \(A\) such that \(\bf R\) is a commutative ring, \(A/C_{A}(G)\) is not a Noetherian \(\bf R\)-module, \(C_{G}(A)=1\), \(G\) is a soluble group. The system of all subgroups \(H \leq G\), for which the quotient modules \(A/C_{A}(H)\) are not Noetherian \(\bf R\)-modules, satisfies the maximal condition. This condition is called the condition \(max-nnd\). The structure of the group \(G\) is described. |
| first_indexed | 2025-12-02T15:43:04Z |
| format | Article |
| id | admjournalluguniveduua-article-650 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:43:04Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-6502018-04-04T09:17:05Z On modules over group rings of soluble groups with commutative ring of scalars Dashkova, O. Yu. a maximal condition on subgroups, a Noetherian module, a soluble group 20F16; 20H25 The author studies an \(\bf R\)\(G\)-module \(A\) such that \(\bf R\) is a commutative ring, \(A/C_{A}(G)\) is not a Noetherian \(\bf R\)-module, \(C_{G}(A)=1\), \(G\) is a soluble group. The system of all subgroups \(H \leq G\), for which the quotient modules \(A/C_{A}(H)\) are not Noetherian \(\bf R\)-modules, satisfies the maximal condition. This condition is called the condition \(max-nnd\). The structure of the group \(G\) is described. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/650 Algebra and Discrete Mathematics; Vol 10, No 2 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/650/184 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | a maximal condition on subgroups a Noetherian module a soluble group 20F16 20H25 Dashkova, O. Yu. On modules over group rings of soluble groups with commutative ring of scalars |
| title | On modules over group rings of soluble groups with commutative ring of scalars |
| title_full | On modules over group rings of soluble groups with commutative ring of scalars |
| title_fullStr | On modules over group rings of soluble groups with commutative ring of scalars |
| title_full_unstemmed | On modules over group rings of soluble groups with commutative ring of scalars |
| title_short | On modules over group rings of soluble groups with commutative ring of scalars |
| title_sort | on modules over group rings of soluble groups with commutative ring of scalars |
| topic | a maximal condition on subgroups a Noetherian module a soluble group 20F16 20H25 |
| topic_facet | a maximal condition on subgroups a Noetherian module a soluble group 20F16 20H25 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/650 |
| work_keys_str_mv | AT dashkovaoyu onmodulesovergroupringsofsolublegroupswithcommutativeringofscalars |