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A generalization of Zariski's main theorem


Author: E. Graham Evans
Journal: Proc. Amer. Math. Soc. 26 (1970), 45-48
MSC: Primary 13.10
DOI: https://doi.org/10.1090/S0002-9939-1970-0260716-8
MathSciNet review: 0260716
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Abstract: This note extends techniques of Peskine and Zariski to prove a generalization of Zariski's Main Theorem which allows infinite integral extensions of finitely generated rings.


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

  • [1] I. S. Cohen and A. Seidenberg, Prime ideals and integral dependence, Bull. Amer. Math. Soc. 52 (1946), 252-261. MR 7, 410. MR 0015379 (7:410a)
  • [2] Wolfgang Krull, Idealtheorie, Zweite, ergänzte Auflage, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 46, Springer-Verlag, Berlin and New York, 1968. MR 37 #5197. MR 0229623 (37:5197)
  • [3] C. Peskine, Une généralisation du ``main theorem'' de Zariski, Bull. Sci. Math. (2) 90 (1966), 119-127. MR 34 #5862. MR 0206037 (34:5862)
  • [4] O. Zariski, Foundations of a general theory of birational correspondences, Trans. Amer. Math. Soc. 53 (1943), 490-542. MR 5, 11. MR 0008468 (5:11b)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0260716-8
Keywords: Integral extensions, isolated primes, prime ideals, conductor
Article copyright: © Copyright 1970 American Mathematical Society

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