Some classes of rings with involution satisfying the standard polynomial of degree 4

Taw Pin Lim

Vol. 85 (1979), No. 1, 125–130

DOI: 10.2140/pjm.1979.85.125

Abstract

The identities valid in the ring of real quaternions are defined in more general classes of rings with involution. With one exception, these classes of rings satisfy the standard polynomial of degree 4 and form a chain under inclusion. There are examples which show that these inclusions are proper. An example of an exterior algebra shows that a ring with involution whose symmetric elements commute does not necessarily satisfy the standard polynomial of degree 4.

Mathematical Subject Classification

Primary: 16A28, 16A28

Secondary: 16A38

Milestones

Received: 1 June 1978

Revised: 2 August 1979

Published: 1 November 1979