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

R. K. Dennis, L. N. Vaserstein

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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