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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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-9672018-05-13T10:43:19Z On the separability of the restriction functor Theohari-Apostolidi, Th. Vavatsoulas, H. separable algebras, strongly graded algebras, restriction functor, induction functor 16W50, 16G30, 16H05 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 \(K\). Lugansk National Taras Shevchenko University 2018-05-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/967 Algebra and Discrete Mathematics; Vol 2, No 3 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/967/496 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-05-13T10:43:19Z |
| collection |
OJS |
| language |
English |
| topic |
separable algebras strongly graded algebras restriction functor induction functor 16W50 16G30 16H05 |
| spellingShingle |
separable algebras strongly graded algebras restriction functor induction functor 16W50 16G30 16H05 Theohari-Apostolidi, Th. Vavatsoulas, H. On the separability of the restriction functor |
| topic_facet |
separable algebras strongly graded algebras restriction functor induction functor 16W50 16G30 16H05 |
| format |
Article |
| author |
Theohari-Apostolidi, Th. Vavatsoulas, H. |
| author_facet |
Theohari-Apostolidi, Th. Vavatsoulas, H. |
| author_sort |
Theohari-Apostolidi, Th. |
| title |
On the separability of the restriction functor |
| title_short |
On the separability of the restriction functor |
| title_full |
On the separability of the restriction functor |
| title_fullStr |
On the separability of the restriction functor |
| title_full_unstemmed |
On the separability of the restriction functor |
| title_sort |
on the separability of the restriction functor |
| description |
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 \(K\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/967 |
| work_keys_str_mv |
AT theohariapostolidith ontheseparabilityoftherestrictionfunctor AT vavatsoulash ontheseparabilityoftherestrictionfunctor |
| first_indexed |
2025-07-17T10:36:49Z |
| last_indexed |
2025-07-17T10:36:49Z |
| _version_ |
1837890126830632960 |