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: 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 $S$.
- 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