A greatest common divisor and a least common multiple of solutions of a linear matrix equation

Abstract

A greatest common divisor and a least common multiple of solutions of a linear matrix equationWe describe the explicit form of a left greatest common divisor and a least common multiple of solutions of a solvable linear matrix equation over a commutative elementary divisor domain. We prove that these left greatest common divisor and least common multiple are also solutions of the same equation.

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

“…of all solutions of a solvable linear equation b = ax (a, b ∈ R) in R is again a solution of the same linear equation. Note that, for rings M n (R) over elementary divisor domains R a positive solution to this problem was done in [14].…”