On the implicit constant fields and key polynomials for valuation algebraic extensions

IF 0.3 4区数学 Q4 MATHEMATICS

Journal of Commutative Algebra Pub Date : 2021-11-29 DOI:10.1216/jca.2022.14.515

Arpan Dutta

引用次数: 2

Abstract

This article is a natural continuation of our previous works [7] and [6]. In this article, we employ similar ideas as in [4] to provide an estimate of IC(K(X)|K, v) when (K(X)|K, v) is a valuation algebraic extension. Our central result is an analogue of [6, Theorem 1.3]. We further provide a natural construction of a complete sequence of key polynomials for v over K in the setting of valuation algebraic extensions.

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关于估值代数扩展的隐式常数域和关键多项式

本文是我们之前的工作[7]和[6]的自然延续。在本文中，我们采用与[4]中类似的思想来提供当(K(X)|K, v)是估值代数扩展时IC(K(X)|K, v)的估计。我们的中心结果类似于[6，定理1.3]。在赋值代数扩展的情况下，我们进一步给出了v / K的键多项式完全序列的自然构造。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Commutative Algebra MATHEMATICS-

CiteScore

0.80

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Commutative Algebra publishes significant results in the area of commutative algebra and closely related fields including algebraic number theory, algebraic geometry, representation theory, semigroups and monoids. The journal also publishes substantial expository/survey papers as well as conference proceedings. Any person interested in editing such a proceeding should contact one of the managing editors.