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FINITE HIGHER COMMUTATORS IN ASSOCIATIVE RINGS

Part of: Rings and algebras with additional structure Modules, bimodules and ideals Rings with polynomial identity

Published online by Cambridge University Press:  27 September 2013

CHARLES LANSKI
CHARLES LANSKI*
Affiliation:
Department of Mathematics, University of Southern California, 3620 South Vermont Avenue, Los Angeles, CA 90089-2532, USA email [email protected]
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Abstract

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If $T$ is any finite higher commutator in an associative ring $R$, for example, $T= [[R, R] , [R, R] ] $, and if $T$ has minimal cardinality so that the ideal generated by $T$ is infinite, then $T$ is in the centre of $R$ and ${T}^{2} = 0$. Also, if $T$ is any finite, higher commutator containing no nonzero nilpotent element then $T$ generates a finite ideal.

Keywords

higher commutatorscommutator identitiesfinite ideals

MSC classification

Secondary: 16W10: Rings with involution; Lie, Jordan and other nonassociative structures 16R50: Other kinds of identities (generalized polynomial, rational, involution) 16D25: Ideals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 3 , June 2014 , pp. 503 - 509
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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