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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.
