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

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Note on multiplicity
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by Daniel Katz PDF
Proc. Amer. Math. Soc. 104 (1988), 1021-1026 Request permission

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 \[ T = \tilde R{[{x_1}/{x_d}, \ldots ,{x_{d - 1}}/{x_d}]_{M\tilde R[{x_1}/{x_d}, \ldots ,{x_{d - 1}}/{x_d}]}}\] and $\tilde R = R/(0:x_d^N),N$ large.
References
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • 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