International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 149-153
doi:10.1155/S0161171291000145
On Galois projective group rings
George Szeto1
and Linjun Ma2
1Mathematics Department, Bradley University, Peoria 61625, Illinois, USA
2Mathematics Department, Zhongshan University, Guangzhou, China
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.