This article is cited in 6 papers

RESEARCH ARTICLE

Some properties of primitive matrices over Bezout B-domain

V. P. Shchedryk

Department of Algebra Pidsryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine 3b Naukova Str. Lviv, 79060, UKRAINE

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.

Keywords: elementary divisor ring, Bezout $B$-domain, canonical diagonal form, transformable matrices, invariants, primitive matrices.

MSC: 15A21

Received: 11.05.2004
Revised: 08.05.2005

Language: English

Bibliographic databases:

• 
•