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system of parameters

Proceedings of the Edinburgh Mathematical Society (1)

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1 results

A Study of the Length Function of Generalized Fractions of Modules
Part of
- Commutative algebra: Homological methods
- Local rings and semilocal rings
Marcel Morales, Pham Hung Quy
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 60 / Issue 3 / August 2017

Published online by Cambridge University Press:

02 November 2016, pp. 721-737
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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.