Finite higher commutators in associative rings

Authors

  • C. Lanski University of Southern California

Keywords:

higher commutators, commutator identities, finite ideals

Abstract

If \( T \) 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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