Vol. 75, No. 2, 1978

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On alternate rings and their attached Jordan rings

Michael Rich

Vol. 75 (1978), No. 2, 511–518

Let A be an alternative ring and Aq its attached quadratic Jordan ring. We show that if A is finitely generated by n generators then Aq is finitely generated by the monomials in A of degree n + 1. It follows that if A is finitely generated then A is nilpotent if and only if Aq is solvable, and for arbitrary A the Levitzki radical of A coincides with the Levitzki radical of Aq. Finally, if A has an involution and H(A,) denotes the -symmetric elements of A then several results known for associative rings connecting properties of H(A,) to those of A apply.

Mathematical Subject Classification 2000
Primary: 17D05
Secondary: 17C50
Received: 16 August 1976
Published: 1 April 1978
Michael Rich