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Preprint Number 501

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501. Krzysztof Krupinski, Predrag Tanovic, Frank Wagner
Around Podewski's conjecture
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Submission date: 30 August 2012.


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.

(Replaces Preprint #412)

Mathematics Subject Classification: Primary 03C60, Secondary 12L12, 20A15, 03C45

Keywords and phrases: Podewski's Conjecture; minimal field; minimal group; valued group

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