Involve: A Journal of Mathematics

  • Involve
  • Volume 7, Number 6 (2014), 769-772.

On commutators of matrices over unital rings

Michael Kaufman and Lillian Pasley

Full-text: Open access

Abstract

Let R be a unital ring and let XMn(R) be any upper triangular matrix of trace zero. Then there exist matrices A and B in Mn(R) such that X=[A,B].

Article information

Source
Involve, Volume 7, Number 6 (2014), 769-772.

Dates
Received: 9 August 2013
Revised: 4 March 2014
Accepted: 8 March 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513733748

Digital Object Identifier
doi:10.2140/involve.2014.7.769

Mathematical Reviews number (MathSciNet)
MR3284883

Zentralblatt MATH identifier
1307.15026

Subjects
Primary: 15A54: Matrices over function rings in one or more variables
Secondary: 16S50: Endomorphism rings; matrix rings [See also 15-XX]

Keywords
trace matrix algebra unital ring

Citation

Kaufman, Michael; Pasley, Lillian. On commutators of matrices over unital rings. Involve 7 (2014), no. 6, 769--772. doi:10.2140/involve.2014.7.769. https://projecteuclid.org/euclid.involve/1513733748


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References

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  • D. Lissner, “Matrices over polynomial rings”, Trans. Amer. Math. Soc. 98 (1961), 285–305.
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  • K. Shoda, “Einige Sätze über Matrizen”, Jap. J. Math. 13 (1936), 361–365. http://msp.org/idx/zbl/0017.05101Zbl 0017.05101