Strongly dependent ordered abelian groups and Henselian fields

Yatir Halevi; Assaf Hasson

doi:https://doi.org/10.1007/s11856-019-1885-3

Strongly dependent ordered abelian groups and Henselian fields

Yatir Halevi, Assaf Hasson

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

Strongly dependent ordered abelian groups have finite dp-rank. They are precisely those groups with finite spines and |{p prime : [G:pG]=∞}|<∞. We apply this to show that if K is a strongly dependent field, then (K, v) is strongly dependent for any Henselian valuation v.

Original language	American English
Pages (from-to)	719-758
Number of pages	40
Journal	Israel Journal of Mathematics
Volume	232
Issue number	2
DOIs	https://doi.org/10.1007/s11856-019-1885-3
State	Published - 1 Aug 2019

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Strongly dependent ordered abelian groups and Henselian fields",

abstract = "Strongly dependent ordered abelian groups have finite dp-rank. They are precisely those groups with finite spines and |{p prime : [G:pG]=∞}|<∞. We apply this to show that if K is a strongly dependent field, then (K, v) is strongly dependent for any Henselian valuation v.",

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AU - Hasson, Assaf

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JF - Israel Journal of Mathematics

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Strongly dependent ordered abelian groups and Henselian fields

Abstract

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