Similarity and commutators of matrices over principal ideal rings

Stasinski, Alexander

doi:10.1090/tran/6402

Similarity and commutators of matrices over principal ideal rings

Stasinski, Alexander

Authors

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

Abstract

We prove that if is a principal ideal ring and is a matrix with trace zero, then is a commutator, that is, for some . This generalises the corresponding result over fields due to Albert and Muckenhoupt, as well as that over due to Laffey and Reams, and as a by-product we obtain new simplified proofs of these results. We also establish a normal form for similarity classes of matrices over PIDs, generalising a result of Laffey and Reams. This normal form is a main ingredient in the proof of the result on commutators.

Citation

Stasinski, A. (2016). Similarity and commutators of matrices over principal ideal rings. Transactions of the American Mathematical Society, 368(4), 2333-2354. https://doi.org/10.1090/tran/6402

Journal Article Type	Article
Acceptance Date	Jan 10, 2014
Online Publication Date	Jul 10, 2015
Publication Date	Apr 1, 2016
Deposit Date	May 2, 2014
Publicly Available Date	Oct 28, 2014
Journal	Transactions of the American Mathematical Society
Print ISSN	0002-9947
Electronic ISSN	1088-6850
Publisher	American Mathematical Society
Peer Reviewed	Peer Reviewed
Volume	368
Issue	4
Pages	2333-2354
DOI	https://doi.org/10.1090/tran/6402

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Copyright Statement
© 2015 American Mathematical Society. First published in Transactions of the American Mathematical Society in Volume 368, Number 4, April 2016, pages 2333-2354, published by the American Mathematical Society.