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FINITE HIGHER COMMUTATORS IN ASSOCIATIVE RINGS
Part of
CHARLES LANSKI
Journal:

Bulletin of the Australian Mathematical Society / Volume 89 / Issue 3 / June 2014

Published online by Cambridge University Press:

27 September 2013, pp. 503-509

Print publication:

June 2014
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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.