Published online by Cambridge University Press: 27 September 2013
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.