Strongly dependent ordered abelian groups and Henselian fields

Yatir Halevi; Assaf Hasson

doi:10.1007/s11856-019-1885-3

Strongly dependent ordered abelian groups and Henselian fields

Yatir Halevi, Assaf Hasson

Department of Mathematics

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

10 Scopus citations

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	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

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s11856-019-1885-3

Cite this

@article{6e2929a3b9b54d13b7bd3572fa17b1d9,

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.",

author = "Yatir Halevi and Assaf Hasson",

note = "Publisher Copyright: {\textcopyright} 2019, The Hebrew University of Jerusalem.",

year = "2019",

month = aug,

day = "1",

doi = "10.1007/s11856-019-1885-3",

language = "English",

volume = "232",

pages = "719--758",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Strongly dependent ordered abelian groups and Henselian fields

AU - Halevi, Yatir

AU - Hasson, Assaf

PY - 2019/8/1

Y1 - 2019/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85070413689&partnerID=8YFLogxK

U2 - 10.1007/s11856-019-1885-3

DO - 10.1007/s11856-019-1885-3

M3 - Article

AN - SCOPUS:85070413689

SN - 0021-2172

VL - 232

SP - 719

EP - 758

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -

Strongly dependent ordered abelian groups and Henselian fields

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this