A criterion for p-henselianity in characteristic p

2015/09/15 by Zoé Chatzidakis, Chatzidakis, Zoé, Milan Perera +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Rings, Modules, and Algebras #math.LO

paper · pdf · doi:10.48550/arxiv.1509.04535

arxiv created 2015/09/15 · arxiv updated 2015/09/16

Abstract

Let p be a prime. In this paper we give a proof of the followingresult: A valued field (K,v) of characteristic p \textgreater 0 isp-henselian if and only if every element of strictly positivevaluation if of the form x^p - x for some x ∈ K.

Related

• Henselianity in the language of rings
• Uniformly defining p-henselian valuations
• Definable henselian valuations in positive residue characteristic
• On logical characterization of henselianity
• NIP henselian valued fields