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2. Right Bézout ring with waist is a right Hermite ring

Author

A. I. Hatalevych

Subjects
Reduced ring, Principal ideal ring, Pure mathematics, Noncommutative ring, Mathematics::Commutative Algebra, Mathematics::Number Theory, General Mathematics, Mathematics::Rings and Algebras, Jacobson radical, Radical of a ring, Algebra, Primitive ring, Simple ring, Computer Science::Symbolic Computation, Von Neumann regular ring, Mathematics
Abstract

We study noncommutative rings in which the Jacobson radical contains a completely prime ideal. It is proved that a right Bezout ring in which the Jacobson radical contains a completely prime ideal is a right Hermite ring. We describe a new class of Bezout rings that are not elementary divisor rings.

Published
2010

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