We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Commutators of trace zero matrices over principal ideal rings.

Stasinski, A. (2018) 'Commutators of trace zero matrices over principal ideal rings.', Israel journal of mathematics., 228 (1). pp. 211-227.


We prove that for every trace zero square matrix A of size at least 3 over a principal ideal ring R, there exist trace zero matrices X, Y over R such that XY−YX = A. Moreover, we show that X can be taken to be regular mod every maximal ideal of R. This strengthens our earlier result that A is a commutator of two matrices (not necessarily of trace zero), and in addition, the present proof is simpler than the earlier one.

Item Type:Article
Full text:(AM) Accepted Manuscript
Download PDF
Publisher Web site:
Publisher statement:The final publication is available at Springer via
Date accepted:19 March 2018
Date deposited:15 June 2018
Date of first online publication:09 August 2018
Date first made open access:09 August 2019

Save or Share this output

Look up in GoogleScholar