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Proceedings of the American Mathematical Society

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

 
 

 

Note on multiplicity


Author: Daniel Katz
Journal: Proc. Amer. Math. Soc. 104 (1988), 1021-1026
MSC: Primary 13H15; Secondary 13B20
DOI: https://doi.org/10.1090/S0002-9939-1988-0929434-8
MathSciNet review: 929434
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Abstract: Let $ (R,M)$ be a local ring with infinite residue field and $ I = ({x_1}, \ldots ,{x_d})R$ an ideal generated by a system of parameters. It is shown that the multiplicity of $ I$ equals the multiplicity of $ IT$ where

$\displaystyle T = \tilde R{[{x_1}/{x_d}, \ldots ,{x_{d - 1}}/{x_d}]_{M\tilde R[{x_1}/{x_d}, \ldots ,{x_{d - 1}}/{x_d}]}}$

and $ \tilde R = R/(0:x_d^N),N$ large.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0929434-8
Keywords: Multiplicity, superficial element, integral closure of an ideal
Article copyright: © Copyright 1988 American Mathematical Society

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