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

Abstract

Solutions of a linear equation b = ax in a homomorphic image of a commutative Bézout domain of stable range 1.5 is 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.