Refaad for Studies, Research and Developement
Field Extension by Galois Theory
25199269 (Print)
25199277 (Online)
Volume 3
Issue 3
2017

0
Field Extension by Galois Theory
132
153
English
Md Tauﬁq NasseefUniversity of Kent, UK taufiq278@gmail.com
Galois Theory, a wonderful part of mathematics with historical roots date back to the solution of cubic and quantic equations in the sixteenth century. However, beside understanding the roots of polynomials, Galois Theory also gave birth to many of the central concepts of modern algebra, including groups and ﬁelds. In particular, this theory is further great due to primarily for two factors: ﬁrst, its surprising link between the group theory and the roots of polynomials and second,the elegance of its presentation. This theory is often descried as one of the most beautiful parts of mathematics. Here I have specially worked on ﬁeld extensions. To understand the basic concept behind fundamental theory, some necessary Theorems, Lammas and Corollaries are added with suitable examples containing Lattice Diagrams and Tables. In principle, I have presented and solved a number of complex algebraic problems with the help of Galois theory which are designed in the context of various rational and complex numbers.
Field Extension; Splitting ﬁelds; Separability; Galois theory
http://www.refaad.com/views/GLM/331.html
http://www.refaad.com/Files/GLM/GLM331.pdf