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ARTIN-SCHREIER EXTENSIONS AND THEIR APPLICATIONS

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Topics in Geometry, Coding Theory and Cryptography

Part of the book series: Algebra and Applications ((AA,volume 6))

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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].

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Authors
  1. Cem Güneri
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  2. Ferruh Özbudak
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Editors and Affiliations

  1. Instituto de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, Brazil

    Arnaldo Garcia

  2. University of Duisburg-Essen, Germany and Sabanci University, Istanbul, Turkey

    Henning Stichtenoth

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Güneri, C., Özbudak, F. (2006). ARTIN-SCHREIER EXTENSIONS AND THEIR APPLICATIONS. In: Garcia, A., Stichtenoth, H. (eds) Topics in Geometry, Coding Theory and Cryptography. Algebra and Applications, vol 6. Springer, Dordrecht . https://doi.org/10.1007/1-4020-5334-4_3

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