The relationships between common multiples of matrices over commutative B´ezout domain of stable range 1.5 [Articol]

Abstract

In the paper, we study common right multiples of matrices over commutative B´ezout domains of stable range 1.5. In particular, for nonsingular matrices of arbitrary order, we indicate the relationships between their common right multiples under certain restrictions on invariant factors. We also establish connections between the invariant factors of the given matrices and the invariant factors of their common right multiples. Furthermore, in this paper we study the structure of the least common right multiple of matrices, specifically its Smith normal form and transforming matrices. As a result, we propose a new method for finding the least common right multiple and establish relationships between the Smith forms of the given matrices and the Smith form of their least common right multiple.