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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Integral ring extensions and prime ideals of infinite rank

Author: William Heinzer
Journal: Proc. Amer. Math. Soc. 28 (1971), 344-346
MSC: Primary 13.80
MathSciNet review: 0276216
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Abstract: An example is constructed showing that for an integral ring extension $ R \subset T$, and a prime ideal $ P$ of $ R$ having infinite rank, it can happen that in $ T$ each prime ideal lying over $ P$ has finite rank.

References [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Éléments de mathématique. Fasc. XXX. Algèbre commutative. Chapitre 5: Entiers. Chapitre 6: Valuations, Actualités Scientifiques et Industrielles, No. 1308, Hermann, Paris, 1964 (French). MR 0194450
  • [2] Robert W. Gilmer, Multiplicative ideal theory, Queen’s Papers in Pure and Applied Mathematics, No. 12, Queen’s University, Kingston, Ont., 1968. MR 0229624
  • [3] Irving Kaplansky, Commutative rings, Allyn and Bacon, Inc., Boston, Mass., 1970. MR 0254021

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Keywords: Integral ring extension, prime ideal, going up property, valuation ring, Prüfer domain
Article copyright: © Copyright 1971 American Mathematical Society