Geodesic
Extremal Valued Fields
Algebra i logika, Tome 43 (2004) no. 5, pp. 582-588 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that every finite-dimensional skew field whose center is an extremal valued field is defect free. We construct an example of an algebraically complete valued field such that a finite-dimensional skew field over it has a non-trivial defect, that is, there exist algebraically complete valued fields that are not extremal.
Keywords: extremal valued field, algebraically complete valued field. 
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     author = {Yu. L. Ershov},
     title = {Extremal {Valued} {Fields}},
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Yu. L. Ershov. Extremal Valued Fields. Algebra i logika, Tome 43 (2004) no. 5, pp. 582-588. http://geodesic.mathdoc.fr/item/AL_2004_43_5_a3/

[1] Yu. L. Ershov, Kratno normirovannye polya, Sib. shkola algebry i logiki, Nauchnaya kniga, Novosibirsk, 2000

[2] F.-V. Kuhlmann, Valuation theory of fields, Abelian groups and modules, Habilitationsschrift, Universität Heidelberg, Heidelberg, 1994

[3] F.-V. Kuhlmann, “Elementary properties of power series fields over finite fields”, J. Symb. Log., 66:2 (2001), 771–791 | DOI | MR | Zbl

[4] L. van den Dries, F.-V. Kuhlmann, “Images of additive polynomials in $F_p((t))$ have the approximation property”, Can. Math. Bull., 45:1 (2002), 71–79 | MR | Zbl

[5] N. Burbaki, Algebra (moduli, koltsa, formy), Nauka, M., 1966 | MR

[6] P. Draxl, “Ostrowski's theorem for Henselian valued skew fields”, J. Rein Angew. Math., 354 (1984), 213–218 | MR | Zbl

[7] R. Pirs, Assotsiativnye algebry, Mir, M., 1986 | MR

[8] N. Jacobson, Finite dimensional division algebras over fields, Springer-Verlag, Berlin, Heidelberg, 1996 | MR | Zbl