Commutator rings
Rings and Algebras
2012-06-11 v3
Abstract
A ring is called a commutator ring if every element is a sum of additive commutators. In this paper we give examples of such rings. In particular, we show that given any ring R, a right R-module N, and a set X, End_R(\bigoplus_X N) and End_R(\prod_X N) are commutator rings if and only if either X is infinite or End_R(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.
Keywords
Cite
@article{arxiv.math/0509148,
title = {Commutator rings},
author = {Zachary Mesyan},
journal= {arXiv preprint arXiv:math/0509148},
year = {2012}
}
Comments
9 pages. The final version contains two new results: Propositions 14 and 20. Also, some of the proofs have been rewritten to improve clarity