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Some results on the degree of imperfection of complete valued fields

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Abstract

We study the relationship between the degree of imperfection of a filed K of characteristic p≠o and its completion\(\hat K\) with respect a rank one valuation v. By looking at the topology defined by v in K, a characterization is given of those valued fields (K,v) such that\(\hat K|K\) is separable, which in its turn is equivalent to the validity of the so-called fundamental equality, in case v is discrete. Also two applications of Baire category theorem to the theory complete valued fields are given.

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Authors and Affiliations

  1. Instituto de Matemática Pura e Aplicada, Rua Luiz de Camões 68, 20.000, Rio de Janeiro, RJ, Brasil

    Gervasio G. Bastos

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  1. Gervasio G. Bastos
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This work is supported by CNPq and by contract FINEP/UFC, IF/224–IF/753.

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Bastos, G.G. Some results on the degree of imperfection of complete valued fields. Manuscripta Math 25, 315–322 (1978). https://doi.org/10.1007/BF01168046

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  • DOI: https://doi.org/10.1007/BF01168046

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