Commutative Bezout domains of stable range 1.5

Victor A. Bovdi, Volodymyr P. Shchedryk

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

A ring R is said to be of stable range 1.5 if for each a,b∈R and 0≠c∈R satisfying aR+bR+cR=R there exists r∈R such that (a+br)R+cR=R. Let R be a commutative domain in which all finitely generated ideals are principal, and let R be of stable range 1.5. Then each matrix A over R is reduced to Smith's canonical form by transformations PAQ in which P and Q are invertible and at least one of them can be chosen to be a product of elementary matrices. We generalize Helmer's theorem about the greatest common divisor of entries of A over R.

Original languageEnglish
Pages (from-to)127-134
Number of pages8
JournalLinear Algebra and Its Applications
Volume568
DOIs
Publication statusPublished - May 1 2019

Keywords

  • Adequate ring
  • Commutative Bezout domain
  • Elementary divisor ring
  • Stable range of a ring

ASJC Scopus subject areas

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

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