A generalization of (−1, 1) rings

Erwin Kleinfeld

Vol. 53 (1974), No. 1, 195–202

DOI: 10.2140/pjm.1974.53.195

Abstract

A ring is defined to be a division ring in case the equations ax = b, and ya = b, have unique solutions for x and y whenever a≠0. It is shown that division rings of characteristic ≠2,3 which satisfy the identities (i) (wx,y,z) + (w,x,(y,z)) = w(x,y,z) + (w,y,z)x, (ii) (x,y,z) + (y,z,x) + (z,x,y) = 0, and (iii) ((x,y),y,y) = 0, are associative.

Mathematical Subject Classification 2000

Primary: 17A30

Milestones

Received: 6 June 1973

Published: 1 July 1974