Galois Subrings of Ore Domains Are Ore Domains

If JR is a ring, and G is a group of automorphisms of R, then R denotes the subring of R consisting of elements of R left fixed by every element of G, and is called the Galois subring corresponding to G. In his paper, Groups acting on hereditary rings, G. M. Bergman has asked if every Galois subring of a right Ore domain corresponding to a finite group is itself right Ore. In this note we show that the answer is affirmative. Henceforth, let R denote a right Ore domain with right quotient field A let G be a finite group of automorphisms, and let G' = exG denote the unique extension of G to D. Then, G' & G under the restriction map