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Similarity and commutators of matrices over principal ideal rings.

Stasinski, Alexander (2016) 'Similarity and commutators of matrices over principal ideal rings.', Transactions of the American Mathematical Society., 368 (4). pp. 2333-2354.


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.

Item Type:Article
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Publisher 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.
Date accepted:10 January 2014
Date deposited:28 October 2014
Date of first online publication:10 July 2015
Date first made open access:No date available

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