Commutator rings

Details Commutator rings Commutator rings

2005-09-07

arxiv.org/abs/math/0509148v3

Bull. Austral. Math. Soc. 74 (2006) 279-288.

Mathematics

Rings and Algebras

9 pages. The final version contains two new results: Propositions 14 and 20. Also, some of the proofs have been rewritten to i

Scientific paper

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.

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