Güneri, Cem and Özbudak, Ferruh
(2007)
*Artin-Schreier extensions and thier applications.*
Topics in Geometry, Coding Theory and Cryptography.
Algebra and Applications; 6 (122).
Springer, Dordrecht, pp. 105-133.
ISBN 9781402053337

Official URL: http://www.springerlink.com/content/k044315288657684/

## Abstract

A Galois extension E/F of fields is called a cyclic extension if the Galois group is cyclic. Assume that p > 0 is the characteristic of our fields and n is the degree of the field extension E/F. If n is relatively prime to p, and there is a primitive n th root of unity in F, then E/F is a Kummer extension, i.e. E = F(y) with y n ∈ F. If n = p, then E/F is an Artin-Schreier extension, i.e. E = F(y) with y p y ∈ F. Finally, if n = p a for a > 1, then the extension E/F can be described in terms of Witt vectors. For these facts, see [34, Section VI.7].

Item Type: | Book Section / Chapter |
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Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Engineering and Natural Sciences |

Depositing User: | Cem Güneri |

Date Deposited: | 08 Dec 2006 02:00 |

Last Modified: | 02 May 2016 11:30 |

URI: | https://research.sabanciuniv.edu/id/eprint/843 |