One of the basic questions of
noncommutative Galois theory is the relation between a ring R and the ring S fixed
by a group of automorphisms of R. This paper explores what happens when the
group is finite and the fixed ring S is assumed to be Noetherian. Easy examples show
that R may not be Noetherian; however, in this paper it is shown that R is
Noetherian with some rather natural assumptions. More precisely we prove the
Theorem 2: Let S be a semiprime ring. Assume that G is a finite group of
automorphisms of S and that S has no |G|-torsion. If SG is left noetherian then S is
left noetherian.
