On partial Galois Azumaya extensions
Let \(\alpha\) be a globalizable partial action of a finite group \(G\) over a unital ring \(R\), \(A=R\star_\alpha G\) the corresponding partial skew group ring, \(R^\alpha\) the subring of the \(\alpha\)-invariant elements of \(R\) and \(\alpha^\star\) the partial inner action of \(G\) (induced by...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/666 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-6662018-04-04T09:24:09Z On partial Galois Azumaya extensions Freitas, Daiane Paques, Antonio partial group action, partial skew group ring, partial Galois extension, partial Galois Azumaya extension 16H05, 16S35, 16W22 Let \(\alpha\) be a globalizable partial action of a finite group \(G\) over a unital ring \(R\), \(A=R\star_\alpha G\) the corresponding partial skew group ring, \(R^\alpha\) the subring of the \(\alpha\)-invariant elements of \(R\) and \(\alpha^\star\) the partial inner action of \(G\) (induced by \(\alpha\)) on the centralizer \(C_A(R)\) of \(R\) in \(A\). In this paper we present equivalent conditions to characterize \(R\) as an \(\alpha\)-partial Galois Azumaya extension of \(R^\alpha\) and \(C_A(R)\) as an \(\alpha^\star\)-partial Galois extension of the center \(C(A)\) of \(A\). In particular, we extend to the setting of partial group actions similar results due to R. Alfaro and G. Szeto [1,2,3]. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/666 Algebra and Discrete Mathematics; Vol 11, No 2 (2011) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/666/200 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-04-04T09:24:09Z |
| collection |
OJS |
| language |
English |
| topic |
partial group action partial skew group ring partial Galois extension partial Galois Azumaya extension 16H05 16S35 16W22 |
| spellingShingle |
partial group action partial skew group ring partial Galois extension partial Galois Azumaya extension 16H05 16S35 16W22 Freitas, Daiane Paques, Antonio On partial Galois Azumaya extensions |
| topic_facet |
partial group action partial skew group ring partial Galois extension partial Galois Azumaya extension 16H05 16S35 16W22 |
| format |
Article |
| author |
Freitas, Daiane Paques, Antonio |
| author_facet |
Freitas, Daiane Paques, Antonio |
| author_sort |
Freitas, Daiane |
| title |
On partial Galois Azumaya extensions |
| title_short |
On partial Galois Azumaya extensions |
| title_full |
On partial Galois Azumaya extensions |
| title_fullStr |
On partial Galois Azumaya extensions |
| title_full_unstemmed |
On partial Galois Azumaya extensions |
| title_sort |
on partial galois azumaya extensions |
| description |
Let \(\alpha\) be a globalizable partial action of a finite group \(G\) over a unital ring \(R\), \(A=R\star_\alpha G\) the corresponding partial skew group ring, \(R^\alpha\) the subring of the \(\alpha\)-invariant elements of \(R\) and \(\alpha^\star\) the partial inner action of \(G\) (induced by \(\alpha\)) on the centralizer \(C_A(R)\) of \(R\) in \(A\). In this paper we present equivalent conditions to characterize \(R\) as an \(\alpha\)-partial Galois Azumaya extension of \(R^\alpha\) and \(C_A(R)\) as an \(\alpha^\star\)-partial Galois extension of the center \(C(A)\) of \(A\). In particular, we extend to the setting of partial group actions similar results due to R. Alfaro and G. Szeto [1,2,3]. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/666 |
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AT freitasdaiane onpartialgaloisazumayaextensions AT paquesantonio onpartialgaloisazumayaextensions |
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2025-12-02T15:36:35Z |
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2025-12-02T15:36:35Z |
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1850411366746161152 |