A Bezout ring with nonzero principal Jacobson radical

Abstract

In this paper, we study a commutative Bezout domain with nonzero Jacobson radical being a principal ideal. It has been proved that such a Bezout domain is a ring of the stable range 1. As a result, we have obtained that such a Bezout domain is a ring over which any matrix can be reduced to a canonical diagonal form by means of elementary transformations of its rows and columns.