Universal Design Description of Cubic Cyclic Fields and an Algorithm for Computing of Minimal Polynomials of Generating Elements

DOI

10.2991/msam-17.2017.29How to use a DOI?

Keywords

gauss sums; integer basis; dirichlet characters; absolutely abelian fields

Abstract

This paper presents an effective description of the universal design cubic cyclic fields and using an algorithm to compute the minimum polynomials generating elements. The calculations are carried out with the use of the properties of Gauss sums corresponding primitive Dirichlet character. Built fundamental and integral basis normal cubic cyclic fields. Necessary and sufficient criterion of element reversibility of totally solid cyclic fields is given here. The different examples of computational exercises of minimal polynomials have been mentioned here. Constructing the model Abelian field, Kronecker-Weber theorem was taken into account; it states that any Abelian extension of the field of rational numbers is in some cyclotomic field. This theorem gives a classification of Abelian fields, and also determines the laws of decomposition, makes it possible to determine the structure of their discriminants and to obtain explicit expressions for the number of ideal classes. The results of the work describe Abelian extensions of a given field. Obtained theoretical data may be used in subsequent studies of algebraic theories, namely, the problem of absolutely Abelian fields.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Amangeldy Bolen
AU  - Maksat Kalimoldayev
AU  - Orken Mamyrbayev
AU  - Kulyash Baisalbayeva
PY  - 2017/03
DA  - 2017/03
TI  - Universal Design Description of Cubic Cyclic Fields and an Algorithm for Computing of Minimal Polynomials of Generating Elements
BT  - Proceedings of the 2017 2nd International Conference on Modelling, Simulation and Applied Mathematics (MSAM2017)
PB  - Atlantis Press
SP  - 127
EP  - 133
SN  - 1951-6851
UR  - https://doi.org/10.2991/msam-17.2017.29
DO  - 10.2991/msam-17.2017.29
ID  - Bolen2017/03
ER  -