A fast algorithm for constructing Arf closure and a conjecture
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.
scientific article; zbMATH DE number 6339754