### Abstract

M. Newman asked whether there is an absolute constant c such that every matrix in SL_{n}R 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 SL_{m}R is the product of a bounded number of commutators for some fixed m ≥ 3, then for all sufficiently large n, every matrix in SL_{n}R is the product of six commutators.

Original language | English (US) |
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Pages (from-to) | 150-161 |

Number of pages | 12 |

Journal | Journal of Algebra |

Volume | 118 |

Issue number | 1 |

DOIs | |

State | Published - Oct 1988 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

*118*(1), 150-161. https://doi.org/10.1016/0021-8693(88)90055-5

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*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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On a question of M. Newman on the number of commutators

AU - Dennis, R. K.

AU - Vaserstein, L. N.

PY - 1988/10

Y1 - 1988/10

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=38249028482&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249028482&partnerID=8YFLogxK

U2 - 10.1016/0021-8693(88)90055-5

DO - 10.1016/0021-8693(88)90055-5

M3 - Article

AN - SCOPUS:38249028482

VL - 118

SP - 150

EP - 161

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -