Right Bézout ring with waist is a right Hermite ring

• Date: 2010
• Main Authors: Gatalevych, A. I., Гаталевич, А. І.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2849
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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....