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Algebra and Discrete Mathematics, 2011, Volume 11, Issue 2, Pages 64–77
(Mi adm11)
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This article is cited in 6 scientific papers (total in 6 papers)
RESEARCH ARTICLE
On partial Galois Azumaya extensions
Daiane Freitasa, Antonio Paquesb a Instituto de Matemática, Estatística e Física, Universidade Federal do Rio Grande, 96201-900,
Rio Grande, RS, Brazil
b Instituto de Matemática, Universidade Federal do Rio Grande do Sul, 91509-900, Porto Alegre, RS, Brazil
Abstract:
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].
Keywords:
partial group action, partial skew group ring, partial Galois extension, partial Galois Azumaya extension.
Received: 25.04.2011 Revised: 06.05.2011
Citation:
Daiane Freitas, Antonio Paques, “On partial Galois Azumaya extensions”, Algebra Discrete Math., 11:2 (2011), 64–77
Linking options:
https://www.mathnet.ru/eng/adm11 https://www.mathnet.ru/eng/adm/v11/i2/p64
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