The class semigroup of a commutative integral domain R is the semigroup S S R of the isomorphism classes of the nonzero ideals of R with the operation induced by multiplication. The aim of this paper is to characterize the Prufer domains R Ž . such that the semigroup S S R is a Clifford semigroup, n
Two Prüfer Domain Counterexamples
✍ Scribed by K.Alan Loper
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 110 KB
- Volume
- 221
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
In that paper, they used the above problem as motivation to ask the related question of when the ideal class group of a Prüfer domain is generated by the classes of the invertible maximal ideals. They gave a very satisfactory answer to this question, but left Boisen's question unsolved. In this article we construct an example which gives a negative answer to Boisen's question. 630
📜 SIMILAR VOLUMES
Let D be a domain with quotient field K. We consider the ring Int D [ f g w x Ž . x K X ; f D : D of integer-valued polynomial rings over D. We completely Ž . characterize the domains D for which Int D is a Prufer ¨-multiplication domain. ᮊ
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