PORTUGALIAE MATHEMATICA Vol. 59, No. 1, pp. 3745 (2002) 

The Invariant Subrings of DemeyerKanzaki Galois ExtensionsLianyong XueDepartment of Mathematics, Bradley University,Peoria, Illinois 61625  U.S.A. Email: lxue@hilltop.bradley.edu Abstract: Let $B$ be a ring with 1, $G$ a finite automorphism group of $B$, $C$ the center of $B$, $B^{G}$ the set of elements in $B$ fixed under each element in $G$. When $B$ is a DeMeyerKanzaki Galois extension of $B^G$ with Galois group $G$, it was shown that a separable subring $S$ of $B$ over $B^G$ is equal to $B^K$ for some subgroup $K$ of $G$ if and only if $CJ_g^{(S)}$ is a faithful $C$module for each $g\not\in K$ where $J_g^{(S)}=\{sg(s)\,\; s\in S\}$. Moreover, the invariant subrings of $C$ over $C^G$ (i.e., $S=C^K$ for some subgroup $K$ of $G$) and of $B\ast G$ over $(B\ast G)^{\bar G}$ are characterized in terms of the faithful $B$module $BJ_g^{(S)}$ and the faithful $C^G$module ${C^G}J_g^{(S)}$ respectively for $g\in G$. Keywords: Galois extensions; center Galois extensions; DeMeyerKanzaki Galois extensions; separable extensions; $H$separable extensions; Azumaya algebras. Classification (MSC2000): 16S35; 16W20. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
© 2002 Sociedade Portuguesa de Matemática
