Let S be a commutative ring
with identity. A group G of automorphisms of S is called locally finite, if for each
s ∈ S, the set {σ(s) : σ ∈ G} is finite. Let R be the subring of G-invariant elements of
S. An R-algebra T is called locally separable if every finite subset of T is contained
in an R-separable subalgebra of T. For an R-separable subalgebra T of S
and for G a locally finite group of automorphisms it is shown that T is the
fixed ring for a group of automorphisms of S. If, in addition, it is assumed
that S has finitely many idempotent elements, then it is shown that any
locally separable subring T of S is the fixed ring for a locally finite group of
automorphisms of S. Examples are included which show the scope of these
theorems.
