On a Class of Free Galois Extensions

X.D. Deng and G. Szeto

Abstract: Let $RG_{f}$ be a projective group algebra over a commutative ring $R$, where $G$ is a finite group and $f$ is a factor set. If $RG_{f}$ is a central Galois $R$-algebra with inner Galois group $G'$ induced by the basis of $RG_{f}$, then there exists a one-to-one correspondence between the set of subgroups $H'$ of $G'$ such that $RH_{f}$ is Galois with a free basis induced by $H'$ and the set of Azumaya subalgebras $B$ over $R$ such that $RG=B(G(B))_{f}$, where $G(B)=\{\alpha\in G\,| \alpha(b)=b\}$ for any $b$ in $B$ and $B(G(B))_{f}$ is a projective group ring over $B$.

Keywords: Projective group rings and algebras; Azumaya algebras; central Galois algebras; Galois extensions.

Classification (MSC2000): 16S35, 16W20

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