Vol. 17, No. 2, 1966

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ISSN: 0030-8730
Some new results on simple algebras

David Joseph Rodabaugh

Vol. 17 (1966), No. 2, 311–317
Abstract

This paper deals with the problem of proving that a simple algebra (finite dimensional) has an identity element. The main result is contained in the following theorem. Let A be a simple algebra (char. 2) in which (x,x,x) = 0 and x3 x = x2 x2. If M is a subset of A such that (A,M,A) = 0 and (M,A,A) (M,A) (A,A,M) M, then M = 0 or there is an identity element in A. This result is then used to prove the three following corollaries (char. 2): (1) A simple power associative algebra with all commutators in the nucleus has an identity; (2) A simple power associative algebra with all associators in the middle center has an identity; (3) A simple antiflexible algebra in which (x,x,x) = 0 and A+ is not nil has an identity.

Mathematical Subject Classification
Primary: 17.20
Milestones
Received: 29 June 1964
Revised: 2 December 1964
Published: 1 May 1966
Authors
David Joseph Rodabaugh