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 6= 0, there exists element r ∈ 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.