Commutators of trace zero matrices over principal ideal rings

Stasinski, A.

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