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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| Date: | 2018 |
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| Main Authors: | , |
| 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/937 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543077523521536 |
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| author | Theohari-Apostolidi, Th. Vavatsoulas, H. |
| author_facet | Theohari-Apostolidi, Th. Vavatsoulas, H. |
| author_sort | Theohari-Apostolidi, Th. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T06:34:59Z |
| 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. |
| first_indexed | 2025-12-02T15:48:23Z |
| format | Article |
| id | admjournalluguniveduua-article-937 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:48:23Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | strongly graded rings Gorenstein orders symmetric algebras 16H05 16G30 16S35 16G10 16W50 Theohari-Apostolidi, Th. Vavatsoulas, H. On strongly graded Gorestein orders |
| title | 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_short | On strongly graded Gorestein orders |
| title_sort | on strongly graded gorestein orders |
| topic | strongly graded rings Gorenstein orders symmetric algebras 16H05 16G30 16S35 16G10 16W50 |
| topic_facet | strongly graded rings Gorenstein orders symmetric algebras 16H05 16G30 16S35 16G10 16W50 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/937 |
| work_keys_str_mv | AT theohariapostolidith onstronglygradedgoresteinorders AT vavatsoulash onstronglygradedgoresteinorders |