Vol. 7, No. 6, 2014

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On commutators of matrices over unital rings

Michael Kaufman and Lillian Pasley

Vol. 7 (2014), No. 6, 769–772
Abstract

Let R be a unital ring and let X Mn(R) be any upper triangular matrix of trace zero. Then there exist matrices A and B in Mn(R) such that X = [A,B].

Keywords
trace, matrix algebra, unital ring
Mathematical Subject Classification 2010
Primary: 15A54
Secondary: 16S50
Milestones
Received: 9 August 2013
Revised: 4 March 2014
Accepted: 8 March 2014
Published: 20 October 2014

Communicated by Chi-Kwong Li
Authors
Michael Kaufman
Kent State University
Kent, OH 44240
United States
Lillian Pasley
North Carolina State University
Raleigh, NC 27695
United States