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On the multiplicity of an integral extension of a local ring

Author: David G. Whitman
Journal: Proc. Amer. Math. Soc. 25 (1970), 145-146
MSC: Primary 13.95
MathSciNet review: 0265354
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Abstract: The following theorem is proved: If $ R$ is a local domain with field of quotients $ F$ and $ S$ is a local integral extension of $ R$ contained in $ F$, then the multiplicity of $ R$ is greater than or equal to the multiplicity of $ S$.

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

  • [1] M. Nagata, Local rings, Interscience Tracts in Pure and Appl. Math., no. 13, Interscience, New York, 1962. MR 27 #5790. MR 0155856 (27:5790)
  • [2] -, The theory of multiplicity in general local rings, Internat. Sympos. Algebraic Number Theory (Tokyo & Nikko, 1955), Science Council of Japan, Tokyo, 1956, pp. 191-226. MR 18, 637. MR 0082966 (18:637b)

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Keywords: Local ring, integral extension, finite integral extension, Hilbert Basis Theorem, multiplicity
Article copyright: © Copyright 1970 American Mathematical Society

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