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 |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/937 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | 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. |
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