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Around Podewski's conjecture

Volume 222 / 2013

Krzysztof Krupiński, Predrag Tanović, Frank O. Wagner Fundamenta Mathematicae 222 (2013), 175-193 MSC: Primary 03C60; Secondary 12L12, 20A15, 03C45. DOI: 10.4064/fm222-2-4


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.


  • Krzysztof KrupińskiInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
  • Predrag TanovićMathematical Institute SANU
    Belgrade, Serbia
  • Frank O. WagnerUniversité de Lyon, CNRS
    Université Lyon 1
    Institut Camille Jordan, UMR 5208
    43 bd du 11 novembre 1918
    69622 Villeurbanne Cedex, France

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