Semiprime ideals in rings with finite group actions

Abstract

Let R be a ring, G a finite group of automorphisms acting on R, and R G the-fixed subring of R. We prove that if R is semiprime with no additive ¦ G¦-torsion, then R is left Goldie if and only if R G is left Goldie. By coupling this with an examination of the prime ideal structures of R G and R, we are able to prove that if ¦G ¦ is invertible in R and R G is left Noetherian, then R satisfies the-ascending chain condition on semiprime ideals, every semiprime factor ring of R is left Goldie, and nil subrings of R are nilpotent. For the pair R G and R, we also consider various other properties of prime and maximal ideals such as lying over, going up, going down, and incomparability.