Commutators and companion matrices over rings of stable rank 1

L. N. Vaserstein, E. Wheland

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

We consider the group GLnA of all invertible n by n matrices over a ring A satisfying the first Bass stable range condition. We prove that every matrix is similar to the product of a lower and upper triangular matrix, and that it is also the product of two matrices each similar to a companion matrix. We use this to show that, when n≥3 and A is commutative, every matrix in SLnA is the product of two commutators.

Original languageEnglish (US)
Pages (from-to)263-277
Number of pages15
JournalLinear Algebra and Its Applications
Volume142
Issue numberC
DOIs
StatePublished - Dec 1990

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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