Around Podewski’s Conjecture

@inproceedings{Krupinski2012AroundPC,
  title={Around Podewski’s Conjecture},
  author={Krzysztof Krupinski and Predrag Tanovic},
  year={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… CONTINUE READING

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Minimale Ringe

  • K. P. Podewski
  • Math. Phys. Semesterber., vol. 22
  • 1973
Highly Influential
6 Excerpts

Generic stability

  • A. Pillay, P. Tanović
  • regularity, and quasiminimality, In: Models…
  • 2011
Highly Influential
3 Excerpts

Minimal fields

  • F. Wagner
  • J. Symbolic Logic, vol. 65/4
  • 2000
1 Excerpt

Model theory of algebraically closed fields

  • A. Pillay
  • In: Model Theory and Algebraic Geometry. An…
  • 1998

On ω1-categorical theories of fields

  • A. Macintyre
  • Fund. Math. vol. 71/1
  • 1971
1 Excerpt

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