On commutators of matrices over unital rings

Kaufman, Michael; Pasley, Lillian

doi:10.2140/involve.2014.7.769

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On commutators of matrices over unital rings

Michael Kaufman and Lillian Pasley

Vol. 7 (2014), No. 6, 769–772

DOI: 10.2140/involve.2014.7.769

Abstract

Let $R$ be a unital ring and let $X \in M_{n} (R)$ be any upper triangular matrix of trace zero. Then there exist matrices $A$ and $B$ in $M_{n} (R)$ 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

Vol. 7, No. 6, 2014