Zur konstruktion bewerteter dicksonscher fastkörper

Ch Karpfinger

doi:10.1007/BF02942040

Zur konstruktion bewerteter dicksonscher fastkörper

Translated title of the contribution: After a short introduction to the valuation theory of nearfields

Ch Karpfinger

Chair of Algorithmic Algebra

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

we give criteria for when a valuation of a skewfield F is also a valuation of the Dickson nearfield F^κ which is derived from F by the coupling K on F. For the construction of examples, a rational function field F = K (t) is given. The set (v) of all prolongations of a valuation u on AT to F is well known. Sufficient conditions are given which guarantee that couplings κ on F and elements ω ε (u) are in this sense compatible so that ω is a valuation of the Dickson nearfield F^κ. Examples demonstrate the results.

Translated title of the contribution	After a short introduction to the valuation theory of nearfields
Original language	German
Pages (from-to)	137-161
Number of pages	25
Journal	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
Volume	75
DOIs	https://doi.org/10.1007/BF02942040
State	Published - 2005

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10.1007/BF02942040

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abstract = "we give criteria for when a valuation of a skewfield F is also a valuation of the Dickson nearfield Fκ which is derived from F by the coupling K on F. For the construction of examples, a rational function field F = K (t) is given. The set (v) of all prolongations of a valuation u on AT to F is well known. Sufficient conditions are given which guarantee that couplings κ on F and elements ω ε (u) are in this sense compatible so that ω is a valuation of the Dickson nearfield Fκ. Examples demonstrate the results.",

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AB - we give criteria for when a valuation of a skewfield F is also a valuation of the Dickson nearfield Fκ which is derived from F by the coupling K on F. For the construction of examples, a rational function field F = K (t) is given. The set (v) of all prolongations of a valuation u on AT to F is well known. Sufficient conditions are given which guarantee that couplings κ on F and elements ω ε (u) are in this sense compatible so that ω is a valuation of the Dickson nearfield Fκ. Examples demonstrate the results.

KW - Extension

KW - Near-field

KW - Simple transe

KW - Valued fields

UR - https://www.scopus.com/pages/publications/33749406420

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DO - 10.1007/BF02942040

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JO - Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

JF - Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

ER -

Zur konstruktion bewerteter dicksonscher fastkörper

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