在与值字段关联的超字段上

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2025-04-25 DOI:10.1016/j.jpaa.2025.107985

Alessandro Linzi , Pierre Touchard

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引用次数: 0

摘要

人们可以用一种自然的方式将有值超域（Hi）i∈i的逆系统与有值域联系起来。相反地，我们研究什么时候这样的系统产生于一个值域。首先，我们推广了Krasner的结果，证明了某些系统的逆极限是严格值超场。其次，我们描述了一个由严格值超场生成亨塞利值场的类哈恩构造。此外，我们在由两个二元函数符号（⊕和⋅）和两个常数符号（0和1）组成的语言中给出了严格值超场理论的公理化。

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On the hyperfields associated to valued fields

One can associate an inverse system of valued hyperfields

{(H_{i})}_{i \in I}

to a valued field in a natural way. We investigate when, conversely, such a system arises from a valued field. First, we extend a result of Krasner by showing that the inverse limit of certain systems are stringent valued hyperfields. Secondly, we describe a Hahn-like construction which yields a henselian valued field from a stringent valued hyperfield. In addition, we provide an axiomatisation of the theory of stringent valued hyperfields in a language consisting of two binary function symbols, ⊕ and ⋅, and two constant symbols, 0 and 1.

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来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.