Quasi-Euclidean duo rings with elementary reduction of matrices

Abstract

We establish necessary and sufficient conditions under which a class of quasi-Euclidean duo rings coincides with a class of rings with elementary reduction of matrices. We prove that a Bezout duo ring with stable range 1 is a ring with elementary reduction of matrices. It is proved that a semiexchange quasi-duo Bezout ring is a ring with elementary reduction of matrices iff it is a duo ring.