Geodesic
Semi-Simple Artinian Rings of Fixed Points
Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 189-190

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Let G be a finite group of automorphisms of the ring R, and let RG denote the ring of fixed points of G in R; that is, RG={x∊R|Xg = x,∀∊ G}. Let |G| denote the order of G. In this note, we prove the following:Theorem.Assume that R has no nilpotent ideals and no |G|-torsion. Then if RG is semi-simple Artinian, R is semi-simple Artinian. 
Cohen, Miriam; Montgomery, Susan. Semi-Simple Artinian Rings of Fixed Points. Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 189-190. doi: 10.4153/CMB-1975-037-9
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