Right Bézout ring with waist is a right Hermite ring - Gatalevych, A. I. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
We study noncommutative rings in which the Jacobson radical contains a completely prime ideal. It is proved that a right Bézout ring in which the Jacobson radical contains a completely prime ideal is a right Hermite ring. We describe a new class of Bézout rings that are not elementary divisor rings.