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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
DOI: https://doi.org/10.1090/S0002-9939-1970-0265354-9
MathSciNet review: 0265354
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Abstract | References | Similar Articles | Additional Information

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?)

  • 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
  • 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

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