Vol. 76, No. 2, 1978

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Scalar dependent algebras in the alternative sense

Joyce Longman and Michael Rich

Vol. 76 (1978), No. 2, 463–470
Abstract

Let R, a not necessarily associative algebra over a field F of characteristic 2, be equipped with a map g : R × R × R F. We show that if R contains a nonzero idempotent and satisfies the identities (1) (xy)z + (yx)z = g(x,y,z)[x(yz) + y(xz)] and (2) (xy)z + (xz)y = g(x,y,z)[x(yz) + x(zy)] then R is an alternative algebra. The methods also apply to other pairs of identities.

Mathematical Subject Classification 2000
Primary: 17D05
Secondary: 17A30
Milestones
Received: 3 May 1977
Revised: 2 November 1977
Published: 1 June 1978
Authors
Joyce Longman
Michael Rich