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A Study of the Length Function of Generalized Fractions of Modules

Published online by Cambridge University Press:  02 November 2016

Marcel Morales
Affiliation:
Université de Grenoble I, Institut Fourier, UMR 5582, BP 74, 38402 Saint-Martin D’Hères, France ([email protected]) ESPE, Université Lyon 1, 5 rue Anselme, 69317 Lyon Cedex, France
Pham Hung Quy
Affiliation:
Department of Mathematics, FPT University, 8 Ton That Thuyet, Hanoi, Vietnam ([email protected])

Abstract

Let be a Noetherian local ring and let M be a finitely generated R-module of dimension d. Let be a system of parameters of M and let be a d-tuple of positive integers. In this paper we study the length of generalized fractions M(1/(x1, … , xd, 1)), which was introduced by Sharp and Hamieh. First, we study the growth of the function

Then we give an explicit calculation for the function in the case in which M admits a certain Macaulay extension. Most previous results on this topic are improved in a clearly understandable way.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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