PORTUGALIAE MATHEMATICA Vol. 56, No. 3, pp. 265272 (1999) 

Notes on Galois Extensions with Inner Galois GroupsXiaoLong Jiang and George SzetoMathematics Department, Zhongshan University,510275 Guangzhou  P. R. CHINA Mathematics Department, Bradley University, Peoria, Illinois, 61625  U.S.A. Abstract: Let $S$ be a ring with 1, $C$ the center of $S$, $G$ a finite inner automorphism group of $S$ of order $n$ for some integer $n$ invertible in $S$ where $G=\{g_{1},g_{2},...,g_{n}\}$ and $g_{i}(s)=U_{i}\,s\,U_{i}^{1}$ for some $U_{i}$ in $S$ and all $s$ in $S$, and $R$ the subring of all elements fixed under each element in $G$. Then, $S$ is a $G$Galois extension of $R$ which is an Azumaya $C$algebra with a Galois system $\{n^{1}U_{i},\,U_{i}^{1}\}$ if and only if $S$ is a projective group ring $RG_{f}$ for some factor set $f$ which is an $H$separable extension of $R$ and $R$ is a separable $C$algebra. Moreover, some correspondence relations are given between certain sets of separable subalgebras of such an $S$. Keywords: Galois extensions; projective group rings; Azumaya algebras; $H$separable extensions. Classification (MSC2000): 16S30, 16W20. Full text of the article:
Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.
© 1999 Sociedade Portuguesa de Matemática
