Actions of finite groups on self-injective rings

David E. Handelman and G. Renault

Vol. 89 (1980), No. 1, 69–80

DOI: 10.2140/pjm.1980.89.69

Abstract

Let G be a finite group of automorphisms of a ring R (with 1), and suppose the order of G is not a zero diviser in R. We denote by R^G the subring of R consisting of elements fixed pointwise by each member of G. We consider, for a class of rings, the questions whether R viewed as a right (or left) R^G-module is finitely generated, and how the type classification of R and R^G relate when R is self-injective regular.

Mathematical Subject Classification

Primary: 16A74, 16A74

Secondary: 16A50

Milestones

Received: 8 May 1979

Revised: 10 September 1979

Published: 1 July 1980