Field Extension by Galois Theory

Volume 3, Issue 3, Article 1 - 2017

Authors: Md Taufiq Nasseef

Copyright © 2017 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract

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.

How To Cite This Article

@article{Nasseef_2017, doi = {10.31559/glm2016.3.3.1}, url = {https://doi.org/10.31559%2Fglm2016.3.3.1}, year = 2017, month = {dec}, publisher = {Refaad for Studies and Research}, volume = {3}, number = {3}, author = {Md Taufiq Nasseef}, title = {Field Extension by Galois Theory}, journal = {General Letters in Mathematics} }
Nasseef, M. T. (2017). Field Extension by Galois Theory. General Letters in Mathematics, 3(3). doi:10.31559/glm2016.3.3.1
Nasseef, Md Taufiq. “Field Extension by Galois Theory.” General Letters in Mathematics 3, no. 3 (December 1, 2017). doi:10.31559/glm2016.3.3.1.
Nasseef, Md Taufiq. “Field Extension by Galois Theory.” General Letters in Mathematics 3, no. 3 (December 1, 2017). doi:10.31559/glm2016.3.3.1.