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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Datum:2018
Hauptverfasser: Theohari-Apostolidi, Th., Vavatsoulas, H.
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2018
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Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/967
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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spelling 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
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