International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 149-153
doi:10.1155/S0161171291000145
On Galois projective group rings
1Mathematics Department, Bradley University, Peoria 61625, Illinois, USA
2Mathematics Department, Zhongshan University, Guangzhou, China
Received 19 September 1989; Revised 10 December 1989
Copyright © 1991 George Szeto and Linjun Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let A be a ring with 1, C the center of A and G′ an
inner automorphism group of A induced by {Uα in A/α in a finite
group G whose order is invertible}. Let AG′ be the fixed subring of
A under the action of G′.If A is a Galcis extension of AG′ with
Galois group G′ and C is the center of the subring ∑αAG′Uα then
A=∑αAG′Uα and the center of AG′ is also C. Moreover, if
∑αAG′Uα is Azumaya over C, then A is a projective group ring.