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Proceedings of the American Mathematical Society

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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] Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers a division of John Wiley & Sons New York-London, 1962. MR 0155856
  • [2] Masayoshi Nagata, The theory of multiplicity in general local rings, Proceedings of the international symposium on algebraic number theory, Tokyo & Nikko, 1955, Science Council of Japan, Tokyo, 1956, pp. 191–226. MR 0082966

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0265354-9
Keywords: Local ring, integral extension, finite integral extension, Hilbert Basis Theorem, multiplicity
Article copyright: © Copyright 1970 American Mathematical Society