Fixed elements of Jordan automorphisms of associative rings

Wallace Smith Martindale, III and Susan Montgomery

Vol. 72 (1977), No. 1, 181–196

DOI: 10.2140/pjm.1977.72.181

Abstract

Let R be an associative ring, and let G be a group of Jordan automorphisms of R. Let R^G be the set of elements in R fixed by all g ∈ G; that is, R^G = {x ∈ R|x^g = x, all g ∈ G}. Although R^G is not necessarily a subring of R, it is a Jordan subring of R. In this paper, we will study the relationship between the structure of R^G as a Jordan ring and the structure of R, where G will usually be a finite group of order |G| and the ring R has no additive |G|-torsion.

Mathematical Subject Classification

Primary: 16A72, 16A72

Milestones

Received: 4 November 1976

Revised: 16 March 1977

Published: 1 September 1977