On ramifications in extensions of rational function fields

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Anbar, Nurdagül (2009) On ramifications in extensions of rational function fields. [Thesis]

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Abstract

Let K (x) be a rational function field, which is a finite separable extension of the rational function field K (z). In the first part of the thesis, we have studied the number of ramified places of K (x) in K (x) =K (z). Then we have given a formula for the ramification index and the different exponent in the extension F (x) over a function field F, where x satisfies an equation f (x) = z for some z 2 F and separable polynomial f (x) 2 K [x]. In fact, this generalizes the well-known formulas for Kummer and Artin- Schreier extensions.
Item Type: Thesis
Uncontrolled Keywords: Function fields. -- Function field extensions. -- Ramification index. -- Different exponent. -- Fonksiyon cisimleri. -- Fonksiyon cisimlerin genişlemeleri. -- Dallanma indexi. -- Fark kuvveti.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: IC-Cataloging
Date Deposited: 14 Oct 2014 11:40
Last Modified: 26 Apr 2022 10:02
URI: https://research.sabanciuniv.edu/id/eprint/24719

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