Galois Groups of Polynomials and the Construction of Finite Fields

S. M. Tudunkaya; A. I. Kiri

doi:doi:10.11648/j.pamj.20120101.12

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Galois Groups of Polynomials and the Construction of Finite Fields

S. M. Tudunkaya, A. I. Kiri

Published in Pure and Applied Mathematics Journal (Volume 1, Issue 1)

Published: 30 December 2012

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Abstract

In this note an attempt was made in constructing finite fields with the aid of Galois groups of polynomials of small degree. The properties of these polynomials, their base fields and their splitting fields werediscussed. From these properties corollaries were developed upon which the constructions were done. The aim was to provide concrete and physical explanations on some aspects of finite fields and Galois theory.

Published in	Pure and Applied Mathematics Journal (Volume 1, Issue 1)
DOI	10.11648/j.pamj.20120101.12
Page(s)	10-16
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2012. Published by Science Publishing Group

Keywords

Group, Galois Group, Galois Extension, Field, Finite Field, Field Extension, Isomorphism

References

[1]	Peters E. M. (1999) Galois Groups of Polynomials of Small Degree. A thesis submitted to the Department of Mathematics, the Pennsylvania State University, the Schreyer Honors College.
[2]	Cherowitz B. (2006) Introduction to Finite Fields, http://www.math.cudenver.edu/wcherowi/vβoutdrd/finflds.html.29k.
[3]	David, J.,(2002). A construction of finite fields. http://www.usna.edu/users/math/wdj/book/node58.html.
[4]	Tudunkaya S. M. and Makanjuola S. O. (2012) Certain Quadratic Extensions. Journal of the Nigerian Association of Mathematical Physics, vol. 22, July issue.
[5]	Tudunkaya S. M. and Makanjuola S. O. (2012) Certain Constrruction of Finite Fields. Journal of the Nigerian Association of Mathematical Physics, vol. 22, November issue.
[6]	Tudunkaya S. M. (2007), Galois Groups of Polynomials of Small Degree and the Construction of Finite Fields. A thesis submitted to the Department of Mathematics, Bayero University, Kano, Nigeria.
[7]	Lang, S.,(2004). Algebra, Graduate Texts in Mathematics (fourth edition). New York, Springer-Verlag.
[8]	Jaisingh L. R. (2004). Abstract Algebra (second edition). McGRAW-HILL, New York.
[9]	Brent, E.,2009. Symmetries of Equations :An introduction to Galois Theory: University of York,York Y010 5DD, England.
[10]	Milne J. S. (2005) Fields & Galois Theory. Erehwon, Taiaroa Publishing.
[11]	Adamson I. T (1964) Introduction to field theory, New York, Interscience publishers Inc.

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APA Style

S. M. Tudunkaya, A. I. Kiri. (2012). Galois Groups of Polynomials and the Construction of Finite Fields. Pure and Applied Mathematics Journal, 1(1), 10-16. https://doi.org/10.11648/j.pamj.20120101.12

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ACS Style

S. M. Tudunkaya; A. I. Kiri. Galois Groups of Polynomials and the Construction of Finite Fields. Pure Appl. Math. J. 2012, 1(1), 10-16. doi: 10.11648/j.pamj.20120101.12

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AMA Style

S. M. Tudunkaya, A. I. Kiri. Galois Groups of Polynomials and the Construction of Finite Fields. Pure Appl Math J. 2012;1(1):10-16. doi: 10.11648/j.pamj.20120101.12

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@article{10.11648/j.pamj.20120101.12,
  author = {S. M. Tudunkaya and A. I. Kiri},
  title = {Galois Groups of Polynomials and the Construction of Finite Fields},
  journal = {Pure and Applied Mathematics Journal},
  volume = {1},
  number = {1},
  pages = {10-16},
  doi = {10.11648/j.pamj.20120101.12},
  url = {https://doi.org/10.11648/j.pamj.20120101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20120101.12},
  abstract = {In this note an attempt was made in constructing finite fields with the aid of Galois groups of polynomials of small degree. The properties of these polynomials, their base fields and their splitting fields werediscussed. From these properties corollaries were developed upon which the constructions were done. The aim was to provide concrete and physical explanations on some aspects of finite fields and Galois theory.},
 year = {2012}
}

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TY  - JOUR
T1  - Galois Groups of Polynomials and the Construction of Finite Fields
AU  - S. M. Tudunkaya
AU  - A. I. Kiri
Y1  - 2012/12/30
PY  - 2012
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DO  - 10.11648/j.pamj.20120101.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 10
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AB  - In this note an attempt was made in constructing finite fields with the aid of Galois groups of polynomials of small degree. The properties of these polynomials, their base fields and their splitting fields werediscussed. From these properties corollaries were developed upon which the constructions were done. The aim was to provide concrete and physical explanations on some aspects of finite fields and Galois theory.
VL  - 1
IS  - 1
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Author Information

S. M. Tudunkaya

Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria
A. I. Kiri

Department of Mathematical Sciences, Bayero University, Kano, Nigeria

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APA Style

S. M. Tudunkaya, A. I. Kiri. (2012). Galois Groups of Polynomials and the Construction of Finite Fields. Pure and Applied Mathematics Journal, 1(1), 10-16. https://doi.org/10.11648/j.pamj.20120101.12

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ACS Style

S. M. Tudunkaya; A. I. Kiri. Galois Groups of Polynomials and the Construction of Finite Fields. Pure Appl. Math. J. 2012, 1(1), 10-16. doi: 10.11648/j.pamj.20120101.12

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AMA Style

S. M. Tudunkaya, A. I. Kiri. Galois Groups of Polynomials and the Construction of Finite Fields. Pure Appl Math J. 2012;1(1):10-16. doi: 10.11648/j.pamj.20120101.12

Copy | Download

@article{10.11648/j.pamj.20120101.12,
  author = {S. M. Tudunkaya and A. I. Kiri},
  title = {Galois Groups of Polynomials and the Construction of Finite Fields},
  journal = {Pure and Applied Mathematics Journal},
  volume = {1},
  number = {1},
  pages = {10-16},
  doi = {10.11648/j.pamj.20120101.12},
  url = {https://doi.org/10.11648/j.pamj.20120101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20120101.12},
  abstract = {In this note an attempt was made in constructing finite fields with the aid of Galois groups of polynomials of small degree. The properties of these polynomials, their base fields and their splitting fields werediscussed. From these properties corollaries were developed upon which the constructions were done. The aim was to provide concrete and physical explanations on some aspects of finite fields and Galois theory.},
 year = {2012}
}

Copy | Download

TY  - JOUR
T1  - Galois Groups of Polynomials and the Construction of Finite Fields
AU  - S. M. Tudunkaya
AU  - A. I. Kiri
Y1  - 2012/12/30
PY  - 2012
N1  - https://doi.org/10.11648/j.pamj.20120101.12
DO  - 10.11648/j.pamj.20120101.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 10
EP  - 16
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20120101.12
AB  - In this note an attempt was made in constructing finite fields with the aid of Galois groups of polynomials of small degree. The properties of these polynomials, their base fields and their splitting fields werediscussed. From these properties corollaries were developed upon which the constructions were done. The aim was to provide concrete and physical explanations on some aspects of finite fields and Galois theory.
VL  - 1
IS  - 1
ER  -

Copy | Download