Vol. 69, No. 2, 1977

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Noetherian fixed rings

Daniel Reuven Farkas and Robert L. Snider

Vol. 69 (1977), No. 2, 347–353

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.

Mathematical Subject Classification
Primary: 16A74, 16A74
Received: 13 October 1976
Published: 1 April 1977
Daniel Reuven Farkas
Robert L. Snider