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Main Author: Kashcheyeva, Olga
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2407.08293
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author Kashcheyeva, Olga
author_facet Kashcheyeva, Olga
contents We consider a rank 1 valuation $ν$ centered in a regular 3-dimensional local ring $R$. We assume that the residue field $k$ of $ν$ is contained in $R$. An algorithm for constructing a generating sequences for $ν$ in $R$ is provided. This is a generalization of our previous algorithm where only valuations of rational rank 1 were considered. We then give a comparison example of a rational rank 3 valuation centered in a ring of polynomials in three variables for which we explicitly compute a set of key polynomials and a generating sequence.
format Preprint
id arxiv_https___arxiv_org_abs_2407_08293
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Generating sequences of rank 1 valuations
Kashcheyeva, Olga
Commutative Algebra
We consider a rank 1 valuation $ν$ centered in a regular 3-dimensional local ring $R$. We assume that the residue field $k$ of $ν$ is contained in $R$. An algorithm for constructing a generating sequences for $ν$ in $R$ is provided. This is a generalization of our previous algorithm where only valuations of rational rank 1 were considered. We then give a comparison example of a rational rank 3 valuation centered in a ring of polynomials in three variables for which we explicitly compute a set of key polynomials and a generating sequence.
title Generating sequences of rank 1 valuations
topic Commutative Algebra
url https://arxiv.org/abs/2407.08293