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Some properties of the Levitzki radical in alternative rings

Part of: Other nonassociative rings and algebras

Published online by Cambridge University Press:  09 April 2009

Michael Rich
Michael Rich
Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122, U.S.A.
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Abstract

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Two local nilpotent properties of an associative or alternative ring A containing an idempotent are shown. First, if A = A11 + A10 + A01 + A00 is the Peirce decomposition of A relative to e then if a is associative or semiprime alternative and 3-torsion free then any locally nilpotent ideal B of Aii generates a locally nilpotent ideal 〈B〉 of A. As a consequence L(Aii) = Aii ∩ L(A) for the Levitzki radical L. Also bounds are given for the index of nilpotency of any finitely generated subring of 〈B〉. Second, if A(x) denotes a homotope of A then L(A) ⊆ L(A(x)) and, in particular, if A(x) is an isotope of A then L(A) = L(A(x)).

MSC classification

Secondary: 17D05: Alternative rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 1 , January 1982 , pp. 52 - 60
Copyright
Copyright © Australian Mathematical Society 1982

References

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