The height of ideals and regular sequences

Craig Huneke; Vijaylaxmi Trivedi

doi:10.1007/bf02677462

The height of ideals and regular sequences

Craig Huneke
, Vijaylaxmi Trivedi

Mathematics

Purdue University

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We prove that given a Noetherian ring R and a finitely generated R-module M, there exists a finite set of prime ideals Λ in R such that the depth of an arbitrary ideal I on M is determined by the height of I modulo each of the primes in Λ. As an application we answer a question raised by the second author and V. Srinivas concerning m-adic approximations of regular sequences in a local ring.

Original language	English
Pages (from-to)	137-142
Number of pages	6
Journal	Manuscripta Mathematica
Volume	93
Issue number	2
DOIs	https://doi.org/10.1007/bf02677462
State	Published - Jun 1997

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title = "The height of ideals and regular sequences",

abstract = "We prove that given a Noetherian ring R and a finitely generated R-module M, there exists a finite set of prime ideals Λ in R such that the depth of an arbitrary ideal I on M is determined by the height of I modulo each of the primes in Λ. As an application we answer a question raised by the second author and V. Srinivas concerning m-adic approximations of regular sequences in a local ring.",

author = "Craig Huneke and Vijaylaxmi Trivedi",

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T1 - The height of ideals and regular sequences

AU - Huneke, Craig

AU - Trivedi, Vijaylaxmi

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N2 - We prove that given a Noetherian ring R and a finitely generated R-module M, there exists a finite set of prime ideals Λ in R such that the depth of an arbitrary ideal I on M is determined by the height of I modulo each of the primes in Λ. As an application we answer a question raised by the second author and V. Srinivas concerning m-adic approximations of regular sequences in a local ring.

AB - We prove that given a Noetherian ring R and a finitely generated R-module M, there exists a finite set of prime ideals Λ in R such that the depth of an arbitrary ideal I on M is determined by the height of I modulo each of the primes in Λ. As an application we answer a question raised by the second author and V. Srinivas concerning m-adic approximations of regular sequences in a local ring.

UR - https://www.scopus.com/pages/publications/0031285587

U2 - 10.1007/bf02677462

DO - 10.1007/bf02677462

M3 - Article

AN - SCOPUS:0031285587

SN - 0025-2611

VL - 93

SP - 137

EP - 142

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

IS - 2

ER -

The height of ideals and regular sequences

Abstract

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