Generating solutions of a linear equation and structure of elements of the Zelisko group

V. A. Bovdi, V. P. Shchedryk

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Solutions of a linear equation b=ax in a homomorphic image of a commutative Bézout domain of stable range 1.5 are developed. It is proved that the set of solutions of a solvable linear equation contains at least one solution that divides the rest, which is called a generating solution. Generating solutions are pairwise associates. Using this result, the structure of elements of the Zelisko group is investigated.

Original languageEnglish
Pages (from-to)55-67
Number of pages13
JournalLinear Algebra and Its Applications
Volume625
DOIs
Publication statusPublished - Sep 15 2021

Keywords

  • Commutative Bézout domain
  • Linear equation
  • Stable range
  • Zelisko group

ASJC Scopus subject areas

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

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