Authors: Krupiński, Krzysztof
Tanović, Predrag 
Wagner, Frank
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Around podewski's conjecture
Journal: Fundamenta Mathematicae
Volume: 222
Issue: 2
First page: 175
Last page: 193
Issue Date: 2-Aug-2013
Rank: M22
ISSN: 0016-2736
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.
Keywords: Minimal field, minimal group | Podewski's conjecture | Valued group
Publisher: Instytut Matematyczny Polskiej Akademii Nauk

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