Semisimple Artinian Rings of Fixed Rings

Abstract

G가 R위에 작용하는 automorphism군일 때 G가 고정시키는 R의 모든 원의 집합을 RG라 하면 RG가 semisimple Artinian 일 때 R도 semisimple Artinain이다.

Let G be a finite group of automorphisms of the ring R, and RG be the ring of fixed points of G in R. Then if RG is semisimple Artinian, R is semisimple Artinian where R has no nlipotent ideals and no

G

torsion.

Let G be a finite group of automorphisms of the ring R, and RG be the ring of fixed points of G in R. Then if RG is semisimple Artinian, R is semisimple Artinian where R has no nlipotent ideals and no

G

torsion.