Vol. 76, No. 1, 1978

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Semisimple nil algebras of type δ

Tim Anderson and Erwin Kleinfeld

Vol. 76 (1978), No. 1, 9–16
Abstract

We prove that a finite dimensional semisimple nil algebra over a field F which satisfies the identity (1 + δ)z(x y) + (1 δ)(x y)z = x(y z) + y(x z), where δ F and δ 12, is anti-commutative. This result permits a further reduction in the problem of classifying those varieties of power-associative algebras over F having the property that squares of ideals are ideals and for which the nil algebras are not pathological.

Mathematical Subject Classification 2000
Primary: 17D10
Milestones
Received: 23 February 1976
Revised: 9 August 1977
Published: 1 May 1978
Authors
Tim Anderson
Erwin Kleinfeld