Commutators of trace zero matrices over principal ideal rings

Stasinski, A.

doi:10.1007/s11856-018-1762-5

Commutators of trace zero matrices over principal ideal rings

Stasinski, A.

Authors

Professor Alexander Stasinski alexander.stasinski@durham.ac.uk
Professor

Abstract

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.

Citation

Stasinski, A. (2018). Commutators of trace zero matrices over principal ideal rings. Israel Journal of Mathematics, 228(1), 211-227. https://doi.org/10.1007/s11856-018-1762-5

Journal Article Type	Article
Acceptance Date	Mar 19, 2018
Online Publication Date	Aug 9, 2018
Publication Date	Oct 31, 2018
Deposit Date	Jun 14, 2018
Publicly Available Date	Aug 9, 2019
Journal	Israel Journal of Mathematics
Print ISSN	0021-2172
Electronic ISSN	1565-8511
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	228
Issue	1
Pages	211-227
DOI	https://doi.org/10.1007/s11856-018-1762-5