Manuscript Information Authors

[1]	Faisal Hussain Nesayef, Department of Mathematics, Faculty of Science, University of Kirkuk, Kirkuk, Iraq.

Abstract

Galois Theory is one of the interesting subjects in Mathematics. It constitutes a link between Polynomials, Fields and Groups. This paper considers manipulation of polynomials, studies and investigates some applications of groups and Fields and their extensions. Polynomials are regarded as an essential tools in the construction of rings and fields. Consequently the ring theory plays the basic role in the study of Galois groups, particular attention has been given to the algebraic polynomials, in terms of their reducible or irreducible properties. This has led to the study of Fields, Extension Fields and the Galois groups. The subject was extensively studied by the great mathematician Galois first. Subsequently many other mathematicians contributed in this field, appreciating Galois' great achievement in this area of mathematics.

Keywords

Basis, Extension Fields, Galois Group, Irreducible Polynomials, Minimal Polynomial, Monic Polynomial, Splitting Fields, Transcendental

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