On a question of M. Newman on the number of commutators

R. K. Dennis, L. N. Vaserstein

Research output: Contribution to journal › Article

42 Citations (Scopus)

Abstract

M. Newman asked whether there is an absolute constant c such that every matrix in SLnR is the product of at most c commutators, where R ranges over euclidean commutative rings and n ≥ 3. We give here a negative answer. However, if for the ring R every matrix in SLmR is the product of a bounded number of commutators for some fixed m ≥ 3, then for all sufficiently large n, every matrix in SLnR is the product of six commutators.

Original languageEnglish (US)
Pages (from-to)150-161
Number of pages12
JournalJournal of Algebra
Volume118
Issue number1
DOIs
StatePublished - Oct 1988

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Commutator
Euclidean ring
Commutative Ring
Ring
Range of data

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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Dennis, R. K. ; Vaserstein, L. N. / On a question of M. Newman on the number of commutators. In: Journal of Algebra. 1988 ; Vol. 118, No. 1. pp. 150-161.
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Dennis, RK & Vaserstein, LN 1988, 'On a question of M. Newman on the number of commutators', Journal of Algebra, vol. 118, no. 1, pp. 150-161. https://doi.org/10.1016/0021-8693(88)90055-5

On a question of M. Newman on the number of commutators. / Dennis, R. K.; Vaserstein, L. N.

In: Journal of Algebra, Vol. 118, No. 1, 10.1988, p. 150-161.

Research output: Contribution to journal › Article

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AB - M. Newman asked whether there is an absolute constant c such that every matrix in SLnR is the product of at most c commutators, where R ranges over euclidean commutative rings and n ≥ 3. We give here a negative answer. However, if for the ring R every matrix in SLmR is the product of a bounded number of commutators for some fixed m ≥ 3, then for all sufficiently large n, every matrix in SLnR is the product of six commutators.

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Dennis RK, Vaserstein LN. On a question of M. Newman on the number of commutators. Journal of Algebra. 1988 Oct;118(1):150-161. https://doi.org/10.1016/0021-8693(88)90055-5

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