On strongly graded Gorestein orders
Let \(G\) be a finite group and let \(\Lambda=\oplus_{g \in G}\Lambda_{g}\) be a strongly \(G\)-graded \(R\)-algebra, where \(R\) is a commutative ring with unity. We prove that if \(R\) is a Dedekind domain with quotient field \(K\), \(\Lambda\) is an \(R\)-order in a separable \(K\)-algebra such...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/937 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-9372018-03-21T06:34:59Z On strongly graded Gorestein orders Theohari-Apostolidi, Th. Vavatsoulas, H. strongly graded rings, Gorenstein orders, symmetric algebras 16H05, 16G30, 16S35, 16G10, 16W50 Let \(G\) be a finite group and let \(\Lambda=\oplus_{g \in G}\Lambda_{g}\) be a strongly \(G\)-graded \(R\)-algebra, where \(R\) is a commutative ring with unity. We prove that if \(R\) is a Dedekind domain with quotient field \(K\), \(\Lambda\) is an \(R\)-order in a separable \(K\)-algebra such that the algebra \(\Lambda_{1}\) is a Gorenstein \(R\)-order, then \(\Lambda\) is also a Gorenstein \(R\)-order. Moreover, we prove that the induction functor \(ind:\ Mod\Lambda_{H}\rightarrow\ Mod\Lambda \) defined in Section 3, for a subgroup \(H\) of \(G\), commutes with the standard duality functor. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/937 Algebra and Discrete Mathematics; Vol 4, No 2 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/937/466 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2018-03-21T06:34:59Z |
| collection |
OJS |
| language |
English |
| topic |
strongly graded rings Gorenstein orders symmetric algebras 16H05 16G30 16S35 16G10 16W50 |
| spellingShingle |
strongly graded rings Gorenstein orders symmetric algebras 16H05 16G30 16S35 16G10 16W50 Theohari-Apostolidi, Th. Vavatsoulas, H. On strongly graded Gorestein orders |
| topic_facet |
strongly graded rings Gorenstein orders symmetric algebras 16H05 16G30 16S35 16G10 16W50 |
| format |
Article |
| author |
Theohari-Apostolidi, Th. Vavatsoulas, H. |
| author_facet |
Theohari-Apostolidi, Th. Vavatsoulas, H. |
| author_sort |
Theohari-Apostolidi, Th. |
| title |
On strongly graded Gorestein orders |
| title_short |
On strongly graded Gorestein orders |
| title_full |
On strongly graded Gorestein orders |
| title_fullStr |
On strongly graded Gorestein orders |
| title_full_unstemmed |
On strongly graded Gorestein orders |
| title_sort |
on strongly graded gorestein orders |
| description |
Let \(G\) be a finite group and let \(\Lambda=\oplus_{g \in G}\Lambda_{g}\) be a strongly \(G\)-graded \(R\)-algebra, where \(R\) is a commutative ring with unity. We prove that if \(R\) is a Dedekind domain with quotient field \(K\), \(\Lambda\) is an \(R\)-order in a separable \(K\)-algebra such that the algebra \(\Lambda_{1}\) is a Gorenstein \(R\)-order, then \(\Lambda\) is also a Gorenstein \(R\)-order. Moreover, we prove that the induction functor \(ind:\ Mod\Lambda_{H}\rightarrow\ Mod\Lambda \) defined in Section 3, for a subgroup \(H\) of \(G\), commutes with the standard duality functor. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/937 |
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AT theohariapostolidith onstronglygradedgoresteinorders AT vavatsoulash onstronglygradedgoresteinorders |
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2025-07-17T10:32:11Z |
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2025-07-17T10:32:11Z |
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