Characterizing finitely generated fields by a single field axiom

IF 8.3 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

ACS Applied Materials & Interfaces Pub Date : 2023-11-01 DOI:10.4007/annals.2023.198.3.4

Philip Dittmann, Florian Pop

引用次数: 1

Abstract

We resolve the Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class there is an explicit first-order sentence which characterizes this field within the class up to isomorphism. Our solution is conditional on resolution of singularities in characteristic two and unconditional in all other characteristics.

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用单域公理描述有限生成域

我们解决了有限生成域的初等等价与同构问题。也就是说，我们证明，对于类中的每个字段，都有一个明确的一阶句子来表征类中的这个字段直至同构。我们的解以特征二的奇点的解为条件，而其他所有特征的解都是无条件的。

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

ACS Applied Materials & Interfaces 工程技术-材料科学：综合

CiteScore

16.00

自引率

6.30%

发文量

4978

审稿时长

1.8 months

期刊介绍： ACS Applied Materials & Interfaces is a leading interdisciplinary journal that brings together chemists, engineers, physicists, and biologists to explore the development and utilization of newly-discovered materials and interfacial processes for specific applications. Our journal has experienced remarkable growth since its establishment in 2009, both in terms of the number of articles published and the impact of the research showcased. We are proud to foster a truly global community, with the majority of published articles originating from outside the United States, reflecting the rapid growth of applied research worldwide.