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

TL;DR

This paper explores the structure of the Zelisko group over certain algebraic domains, providing explicit descriptions of its elements in specific cases, advancing understanding of its algebraic properties.

Contribution

It offers a new explicit characterization of Zelisko group elements over homomorphic images of Bézout domains with stable rank 1.5, extending previous work.

Findings

Explicit form of Zelisko group elements over homomorphic images of Bézout domains.

Structural insights into the Zelisko group over domains of stable rank 1.5.

Extension of previous investigations on the Zelisko group.

Abstract

We continue our previous investigation of the Zelisko group of a matrix over B\'ezout domains. The explicit form of elements of this group over homomorphic image of B\'ezout domain of stable rank 1.5 is described.