On the separability of the restriction functor
Let \(G\) be a group, \(\Lambda=\bigoplus_{\sigma \in G}\Lambda_{\sigma}\) a strongly graded ring by \(G\), \(H\) a subgroup of \(G\) and \(\Lambda_{H}=\bigoplus_{\sigma \in H}\Lambda_{\sigma}\). We give a necessary and sufficient condition for the ring \(\Lambda/\Lambda_{H}\) to be separable, gener...
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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/967 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | Let \(G\) be a group, \(\Lambda=\bigoplus_{\sigma \in G}\Lambda_{\sigma}\) a strongly graded ring by \(G\), \(H\) a subgroup of \(G\) and \(\Lambda_{H}=\bigoplus_{\sigma \in H}\Lambda_{\sigma}\). We give a necessary and sufficient condition for the ring \(\Lambda/\Lambda_{H}\) to be separable, generalizing the corresponding result for the ring extension \(\Lambda/\Lambda_{1}\). As a consequence of this result we give a condition for \(\Lambda\) to be a hereditary order in case \(\Lambda\) is a strongly graded by finite group \(R\)-order in a separable \(K\)-algebra, for \(R\) a Dedekind domain with quotient field \(K\). |
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