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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, Algèbre commutative, Chapitres 5, 6, Actualités Sci. Indust., no. 1308, Hermann, Paris, 1964. MR 33 #2660. MR 0194450 (33:2660)
  • [2] R. Gilmer, Multiplicative ideal theory, Queen's Papers in Pure and Appl. Math., no. 12, Queen's University, Kingston, Ont., 1968. MR 37 #5198. MR 0229624 (37:5198)
  • [3] I. Kaplansky, Commutative rings, Allyn and Bacon, Boston, Mass., 1970. MR 0254021 (40:7234)

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

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