Around Podewski's conjecture

• Autorzy: Krzysztof Krupiński , Predrag Tanović , Frank O. Wagner
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 20A15: Applications of logic to group theory
• 03C60: Model-theoretic algebra
• 12L12: Model theory
• 03C45: Classification theory, stability and related concepts

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 222
• Numer: 2
• Strony: 175-193

Daty

wydano

2013

Twórcy

autor

Krzysztof Krupiński

• Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Predrag Tanović

• Mathematical Institute SANU, Belgrade, Serbia

autor

Frank O. Wagner

• Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, UMR 5208, 43 bd du 11 novembre 1918, 69622 Villeurbanne Cedex, France

Identyfikatory

DOI

10.4064/fm222-2-4