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
Full-text PDF Free Access
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
M. Nagata, Local rings, Interscience Tracts in Pure and Appl. Math., no. 13, Interscience, New York, 1962. MR 27 #5790.
---, 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.
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13.95
Retrieve articles in all journals with MSC: 13.95