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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.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s11856-018-1762-5
Publisher statement:The final publication is available at Springer via https://doi.org/10.1007/s11856-018-1762-5.
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

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