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Semi-Simple Artinian Rings of Fixed Points

Published online by Cambridge University Press:  20 November 2018

Miriam Cohen  and
Susan Montgomery
Miriam Cohen
Affiliation:
Tel-Aviv University, Ramat Aviv, Israel
Susan Montgomery
Affiliation:
University of Southern California, Los Angeles, California
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 189 - 190
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Bergman, G. and Isaacs, I. M., Rings with Fixed-Point-Free Group Actions, Proc. London Math. Soc, 27 (1973), pp. 69-87.Google Scholar
2. Cohen, M., Semi-prime Goldie Centralizers, Israel Journal, (to appear).Google Scholar
3. Harchenko, V. K., Galois Extensions and Rings of Fractions, (Russian abstract), 2nd All- Union Symposium in Ring, Algebra and Module Theory, Kishinyov (1974).Google Scholar