Arf closure relative to a divisorial valuation and transversal curves
Arf closure relative to a divisorial valuation and transversal curves
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Arf 闭合相对于除数估值和横向曲线
DOI：
10.2307/2374934
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
Julio Antonio Castellanos Peñuela
中科院分区：
文献类型：
--
作者：
A. Campillo;Julio Antonio Castellanos Peñuela
如果离散评估环 Rv 的子环满足 C. Arf 大约 45 年前首次考虑的特定条件，则称为 Rv-Arf 环。设 A 为 Rv 的任意子环，I 为 A 的理想。解释了 A 沿估值 v 在 I 处爆炸的操作，以及 A 相对于 v 的 Arf 闭包。研究了它们的代数结构和主要性质。结果表明，在某些假设下，Rv 的 Arf 子环族满足升链条件。研究了Rv的Arf子环与Rv的严格闭子环之间的关系。最后一节给出了 Arf 闭包的几何解释。
A subring of a discrete valuation ring Rv is called an Rv-Arf ring if it satisfies a certain condition first considered by C. Arf some forty-five years ago. Let A be any subring of Rv and let I be an ideal of A. The operation of the blow up of A at I along the valuation v, and the Arf closure of A with respect to v are explained. Their algebraic structure and main properties are studied. It is shown that, under some assumptions, the family of Arf subrings of Rv satisfies the ascending chain condition. The relation between Arf subrings of Rv and strictly closed subrings of Rv is studied. In the last section the geometrical interpretation of the Arf closure is given.