2022•Carpathian Mathematical PublicationsOpen access

A Bezout ring with nonzero principal Jacobson radical

Andry Gatalevych, A.A. Dmytruk

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.

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Key concepts: Jacobson radical, Mathematics, Commutative ring, Principal ideal, Ring (chemistry), Diagonal, Domain (mathematical analysis), Ideal (ethics)