Alternative rings whose symmetric elements are nilpotent or a right multiple is a symmetric idempotent

G. P. Wene

Vol. 90 (1980), No. 2, 483–492

DOI: 10.2140/pjm.1980.90.483

Abstract

Osborn characterizes those associative rings with involutions in which each symmetric element is nilpotent or invertible. Analogous results are obtained for alternative rings. The restriction is further relaxed to require only that each symmetric element is nilpotent or some multiple is a symmetric idempotent.

Mathematical Subject Classification 2000

Primary: 17D05

Milestones

Received: 20 April 1978

Revised: 14 August 1979

Published: 1 October 1980