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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 1, pp. 136–138, January, 2010.
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Hatalevych, A.I. Right Bézout ring with waist is a right Hermite ring. Ukr Math J 62, 151–154 (2010). https://doi.org/10.1007/s11253-010-0339-1
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DOI: https://doi.org/10.1007/s11253-010-0339-1