Similarity and commutators of matrices over principal ideal rings
| Autor: | Alexander Stasinski |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Principal ideal ring
Discrete mathematics Pure mathematics Similarity (geometry) Trace (linear algebra) Applied Mathematics General Mathematics Zero (complex analysis) Commutator (electric) Mathematics - Rings and Algebras Mathematical proof law.invention Matrix (mathematics) Rings and Algebras (math.RA) law Principal ideal FOS: Mathematics Mathematics |
| Zdroj: | Transactions of the American Mathematical Society, 2016, Vol.368(4), pp.2333-2354 [Peer Reviewed Journal] |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/tran/6402 |
| Popis: | We prove that if R is a principal ideal ring and A\in\M_n(R) is a matrix with trace zero, then A is a commutator, that is, A=XY-YX for some X,Y\in\M_n(R). This generalises the corresponding result over fields due to Albert and Muckenhoupt, as well as that over Z 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. 23 pages; minor corrections |
| Databáze: | OpenAIRE |
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