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Preprint Number 534
534. Tomasz Gogacz and Krzysztof Krupinski On regular groups and fields E-mail: , Submission date: 16 November 2012. Abstract: Regular groups and fields are common
generalizations of minimal and
quasi-minimal groups and fields, so the conjectures that minimal or
quasi-minimal fields are algebraically closed have their common generalization
to the conjecture that each regular field is algebraically closed. Standard
arguments show that a generically stable regular field is algebraically closed.
Let K be a regular field which is not generically stable and let p be its
global generic type. We observe that if K has a finite extension L of
degree n, then p^{(n)} has unbounded orbit under the action of the
multiplicative group of L. Mathematics Subject Classification: 03C60, 12L12, 20A15, 20E06, 03C45 Keywords and phrases: |

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