Some properties of primitive matrices over Bezout B-domain

Abstract

The properties of primitive matrices (matrices for which the greatest common divisor of the minors of maximal order is equal to 1) over Bezout B - domain, i.e. commutative domain finitely generated principal ideal in which for all \(a, b, c\) with \((a, b, c)=1, c\neq 0,\) there exists element \(r\in R\), such that \((a+rb, c)=1\) is investigated. The results obtained enable to describe invariants transforming matrices, i.e. matrices which reduce the given matrix to its canonical diagonal form.