Archive
2020, Volume 9
2019, Volume 8
2018, Volume 7
2017, Volume 6
2016, Volume 5
2015, Volume 4
2014, Volume 3
2013, Volume 2
2012, Volume 1




Volume 1, Issue 1, December 2012, Page: 10-16
Galois Groups of Polynomials and the Construction of Finite Fields
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
Received: Dec. 31, 2012;       Published: Dec. 30, 2012
DOI: 10.11648/j.pamj.20120101.12      View  4122      Downloads  208
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.
Keywords
Group, Galois Group, Galois Extension, Field, Finite Field, Field Extension, Isomorphism
To cite this article
S. M. Tudunkaya, A. I. Kiri, Galois Groups of Polynomials and the Construction of Finite Fields, Pure and Applied Mathematics Journal. Vol. 1, No. 1, 2012, pp. 10-16. doi: 10.11648/j.pamj.20120101.12
Reference
[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.
Browse journals by subject