Publication details for Alexander StasinskiStasinski, Alexander (2016). Similarity and commutators of matrices over principal ideal rings. Transactions of the American Mathematical Society 368(4): 2333-2354.
- Publication type: Journal Article
- ISSN/ISBN: 0002-9947, 1088-6850
- DOI: 10.1090/tran/6402
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
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.