Rings of simple range 2

TL;DR

This paper introduces rings of simple range 2 and develops a diagonal reduction theory for matrices over Bezout domains, establishing a key equivalence related to elementary divisor rings.

Contribution

It defines rings of simple range 2 and proves that invariant Bezout domains are elementary divisor rings if and only if they are rings of simple range 2.

Findings

Invariant Bezout domain is an elementary divisor ring iff it is a ring of simple range 2

Develops a diagonal reduction theory for matrices over Bezout domains

Introduces the concept of rings of simple range 2

Abstract

We introduce the concept of rings of simple range 2. Based on this concept, we build a theory diagonal reduction of matrices over Bezout domain. In particular we show that invariant Bezout domain is an elementary divisor ring if and only if it is a rings of simple range 2.