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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory