Vol. 89, No. 1, 1980

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Actions of finite groups on self-injective rings

David E. Handelman and G. Renault

Vol. 89 (1980), No. 1, 69–80

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 RG 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) RG-module is finitely generated, and how the type classification of R and RG relate when R is self-injective regular.

Mathematical Subject Classification
Primary: 16A74, 16A74
Secondary: 16A50
Received: 8 May 1979
Revised: 10 September 1979
Published: 1 July 1980
David E. Handelman
G. Renault