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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| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/650 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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. |
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