On $H$-separable and Galois Extensions of Rings

George Szeto

Abstract: Let $S$ be a ring with $1$, $G$ a finite automorphism group of $S$ of order $n$, and $S^{*}G$ the skew group ring of $G$ over $S$. Assume $n$ is a unit in $S$. If $S$ is a $G$-Galois and an $H$-separable extension of $S^{G}$, then $S^{*}G$ is an Azumaya algebra if and only if $S$ is Azumaya. Moreover, the structure theorem for a central Galois algebra of F.R. DeMeyer is generalized to a $G$-Galois extension with an inner Galois group.

Keywords: Galois extensions of rings; $H$-separable extensions; Azumaya algebras; skew group rings.

Classification (MSC2000): 16S30, 16W20

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