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Fundamenta MathematicaeVolume 222, Issue 2, 2013, Pages 175-193

Around podewski's conjecture(Article)(Open Access)

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  • aInstytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • bUniversité de Lyon, CNRS, Université Lyon 1, 69622 Villeurbanne Cedex, France
  • cMathematical Institute SANU, Belgrade, Serbia

Abstract

A long-standing conjecture of Podewski states that every minimal field is algebraically closed. Known in positive characteristic, it remains wide open in characteristic zero. We reduce Podewski's conjecture to the (partially) ordered case, and we conjecture that such fields do not exist. We prove the conjecture in case the incomparability relation is transitive (the almost linear case). We also study minimal groups with a (partial) order, and give a complete classification of almost linear minimal groups as certain valued groups. ©Instytut Matematyczny PAN, 2013.

Author keywords

Minimal field, minimal groupPodewski's conjectureValued group
  • ISSN: 00162736
  • Source Type: Journal
  • Original language: English
  • DOI: 10.4064/fm222-2-4
  • Document Type: Article

  Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, Poland
© Copyright 2013 Elsevier B.V., All rights reserved.

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