Products of involutory matrices over rings

F. A. Arlinghaus, L. N. Vaserstein, Hong You

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let αε{lunate}GLn A be a matrix over a commutative ring A with 1 such that (det α)2 = 1. If α is cyclic, it can be written as a product of at most three involutions. When A satisfies the first Bass stable range condition, then α can be written as a product of at most five involutions. If in addition either n ≤ 3 or n = 4 and det α = -1, then α can be written as a product of at most four involutions. When A is a Dedekind ring of arithmetic type, the number of involutions needed to express α is uniformly bounded for any n ≥ 3. When A = C[x] the number of involutions is unbounded for any n ≥ 2.

Original languageEnglish (US)
Pages (from-to)37-47
Number of pages11
JournalLinear Algebra and Its Applications
Volume229
Issue numberC
DOIs
StatePublished - Nov 1 1995

All Science Journal Classification (ASJC) codes

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

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