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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 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
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by David G. Whitman
Proc. Amer. Math. Soc. 25 (1970), 145-146
DOI: https://doi.org/10.1090/S0002-9939-1970-0265354-9
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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
  • Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), 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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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • 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