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

V. A. Bovdi; V. P. Shchedryk

doi:10.1016/j.laa.2021.04.019

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

V. A. Bovdi, V. P. Shchedryk

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Citations (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 language	English
Pages (from-to)	55-67
Number of pages	13
Journal	Linear Algebra and Its Applications
Volume	625
DOIs	https://doi.org/10.1016/j.laa.2021.04.019
Publication status	Published - Sept 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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10.1016/j.laa.2021.04.019

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N2 - 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.

AB - 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.

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KW - Linear equation

KW - Stable range

KW - Zelisko group

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

Abstract

Keywords

ASJC Scopus subject areas

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