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.