Conditions for stable range of an elementary divisor rings

Abstract

Using the concept of ring of Gelfand range 1 we proved that a commutative Bezout domain is an elementary divisor ring iff it is a ring of Gelfand range 1. Obtained results give a solution of problem of elementary divisor rings for different classes of commutative Bezout domains, in particular, $P{M}^{\ast }$, local Gelfand domains and so on.

Cited by in corpus (1)

• Elementary matrix reduction over Bezout duo rings