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.
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.1090/tran/6402|
|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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