Elementarily equivalent fields with inequivalent perfect closures
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- by Carlos R. Videla PDF
- Proc. Amer. Math. Soc. 99 (1987), 171-175 Request permission
Abstract:
We give a counterexample to the following conjecture due to L. V. den Dries: Let $F,L$ be two fields of characteristic $p$. If $F \equiv L$ then ${F^1}/{p^\infty } \equiv {L^1}/{p^\infty }$.References
- G. L. Cherlin, Definability in power series rings of nonzero characteristic, Models and sets (Aachen, 1983) Lecture Notes in Math., vol. 1103, Springer, Berlin, 1984, pp. 102–112. MR 775690, DOI 10.1007/BFb0099383
- I. R. Shafarevich, Basic algebraic geometry, Springer Study Edition, Springer-Verlag, Berlin-New York, 1977. Translated from the Russian by K. A. Hirsch; Revised printing of Grundlehren der mathematischen Wissenschaften, Vol. 213, 1974. MR 0447223 L. Van den Dries, Model theory of fields, Thesis, Utrecht 1978, Stellingen 4.
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 171-175
- MSC: Primary 12L12; Secondary 03C60, 12F99
- DOI: https://doi.org/10.1090/S0002-9939-1987-0866447-8
- MathSciNet review: 866447