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

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 so...

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Bibliographic Details
Published in:Linear algebra and its applications 2021-09, Vol.625, p.55-67
Main Authors: Bovdi, V.A., Shchedryk, V.P.
Format: Article
Language:English
Subjects:
Commutative Bézout domain
Linear algebra
Linear equation
Linear equations
Stable range
Zelisko group
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Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2021.04.019