Similarity and commutators of matrices over principal ideal rings

Stasinski, Alexander

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