Fields: Algebraically closed and others
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Publication:1197358
DOI10.1007/BF02567077zbMath0767.12001MaRDI QIDQ1197358
Publication date: 16 January 1993
Published in: Manuscripta Mathematica (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/155716
sums of squaresPythagorean fieldsEuclidean fieldsselected bibliographyalgebraic extensionsexpository paperalgebraically closed fieldsreal fieldsformal power series fieldsPythagorean generalized power series fields
Algebraic field extensions (12F05) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Ordered fields (12J15) Valued fields (12J10) Power series rings (13J05) Research exposition (monographs, survey articles) pertaining to field theory (12-02)
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Cites Work
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- Equivalent forms of Hensel's lemma
- Fields of generalized power series
- Rings of generalized power series: Nilpotent elements
- Rings of generalized power series. II: Units and zero-divisors
- Special properties of generalized power series
- Wohlgeordnete Untermengen in totalgeordneten Gruppen. Mit einer Anwendung auf Potenzreihenkörper
- The Absolute Galois Group of a Rational Function Field in Characteristic Zero is a Semi-Direct Product
- Algebraically Closed Fields Analogous to Fields of Puiseux Series
- The Pythagorean closure of fields.
- Allgemeine Bewertungstheorie.
- A Note on the Quotient Field of the Domain DX
- An algebraically closed field
- On Ordered Division Rings