Vol. 36, No. 3, 1971

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Speciality of quadratic Jordan algebras

Kevin Mor McCrimmon

Vol. 36 (1971), No. 3, 761–773

In this paper we extend to quadratic Jordan algebras certain results due to P. M. Cohn giving conditions under which a Jordan algebra is special, the most important of ihese being the Shirshov-Cohn Theorem that a Jordan algebra with two generators and no extreme radical is always special. We also prove that the free algebra on two generators x, y modulo polynomial relations p(x) = 0,q(y) = 0 is special, and by taking a particular p(x) we show that most of the properties of the Peirce decomposition of a Jordan algebra relative to a supplementary family of orthogonal idempotents follow immediately from the analogous properties of Peirce decompositions in associative algebras.

Mathematical Subject Classification 2000
Primary: 17C10
Received: 30 June 1970
Published: 1 March 1971
Kevin Mor McCrimmon