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Bézout SP-Domains
Abstract
SP-domains were first introduced by Vaughan and Yeagy (1978) as generalizations of Dedekind domains. In particular, they showed that an SP-domain is an almost Dedekind domain. Later, Olberding (20057.
Olberding , B. ( 2005 ). Factorization into radical ideals . In: Chapman , S. , ed. Arithmetical Properties of Commutative Rings and Monoids . Lect. Notes Pure Appl. Math. Vol. 241 . Chapman & Hall , pp. 363 – 377 .
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View all references) gave a complete characterization of SP-domains within the class of almost Dedekind domains. This article characterizes Bézout SP-domains using the order structure of the group of divisibility of an integral domain. We use this information to construct a Bézout SP-domain with zero Jacobson radical.
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- Available online: 07 May 2007
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- a Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio, USA
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