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Similarity and commutators of matrices over principal ideal rings

Stasinski, Alexander

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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
Public URL https://durham-repository.worktribe.com/output/1433487

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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.





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