Finite higher commutators in associative rings

C. Lanski

Finite higher commutators in associative rings

Authors

C. Lanski University of Southern California

Keywords:

higher commutators, commutator identities, finite ideals

Abstract

$T$ is any finite higher commutator in a 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 center 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. DOI: 10.1017/S0004972713000890

Author Biography

C. Lanski, University of Southern California

Professor of Mathematics

Published

2014-03-25

Issue

Vol. 89 No. 3 (2014)

Section

Articles

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