The fixed subrings of a finite group of automorphisms of \(\aleph_0\)-continuous regular rings (Q2266103)

Let G be a finite group of automorphisms of a ring R. Let \(R^ G\) be the fixed subring of R under G. It is known that if R is a left self-injective regular ring and the order \(| G|\) of G is invertible in R, then \(R^ G\) is also a left self-injective regular ring. The author proves that if R is a left \(\aleph_ 0\)-continuous, left \(\aleph_ 0\)-injective regular ring and \(| G|\) is invertible in R, then \(R^ G\) is a left \(\aleph_ 0\)-continuous, \(\aleph_ 0\)-injective regular ring. He also proves that if S is the maximal left \(\aleph_ 0\)-quotient ring of R, \(S^ G\) is the maximal left, \(\aleph_ 0\)-quotient ring of \(R^ G\).