Vol. 53, No. 1, 1974

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A generalization of (1, 1) rings

Erwin Kleinfeld

Vol. 53 (1974), No. 1, 195–202
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 a0. 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
Authors
Erwin Kleinfeld