A fast algorithm for constructing Arf closure and a conjecture
type: Item
instance of: scholarly article
title: A fast algorithm for constructing Arf closure and a conjecture
zbMATH Open document ID: 1298.14031
author: Feza Arslan
author: Nil Şahin
published in: Journal of Algebra
publication date: 2014-09-04T00:00:00Z
reviewed by: Gerhard Pfister
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 32B10
zbMATH DE Number: 6339754
zbMATH Keywords: branch
zbMATH Keywords: Arf ring
zbMATH Keywords: Arf closure
zbMATH Keywords: Arf semigroup
Wikidata QID: Q123026124
describes a project that uses: SINGULAR
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2014.06.023
OpenAlex ID: W2004488515
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DOI: 10.1016/J.JALGEBRA.2014.06.023
review text: Let \(R=kx_1(t), \ldots, x_n (t)\subseteq kt\) such that \(\dim_k kt/R<\infty\). Let \(\Gamma(R)\) be the semi--group of \(R\). For any \(n\in \Gamma(R)\) choose \(S_n\in R\) such that \(\text{ord}(S_n)=n\). \(R\) is called Arf ring if \(\{rS_n^{-1}|\text{ord} (r)\geq n\}\) is a ring for alle \(n\in \Gamma(R)\). The Arf closure of \(R\) is the smallest Arf ring containing \(R\).NEWLINENEWLINEAn algorithm is given for computing the Arf closure. The relation between rings with the same Arf closure is studied.
description: scientific article; zbMATH DE number 6339754