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Commutator rings

Published online by Cambridge University Press:  17 April 2009

Zachary Mesyan
Zachary Mesyan
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, United States of America e-mail: zak@math.berkeley.edu
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A ring is called a commutator ring if every element is a sum of additive commutators. In this note we give examples of such rings. In particular, we show that given any ring R, a right R-module N, and a nonempty set Ω, EndR(⌖ΩN) and EndR(ΠΩN) are commutator rings if and only if either Ω is infinite or EndR(N) is itself a commutator ring. We also prove that over any ring, a matrix having trace zero can be expressed as a sum of two commutators.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 2 , October 2006 , pp. 279 - 288
Copyright
Copyright © Australian Mathematical Society 2006

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