Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 54, No. 4, pp. 399-405 (1997)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



On $H$-separable and Galois Extensions of Rings

George Szeto

Mathematics Department, Bradley University,
Peoria, Illinois 61625 - U.S.A.

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

Full text of the article:

Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.

© 1997 Sociedade Portuguesa de Matemática
© 1997–2007 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition