Extension fields and Galois Theory

B.Nithya; Dr.V. Ramadoss

doi:https://doi.org/10.14445/22315373/IJMTT-V65I7P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 7 | Year 2019 | Article Id. IJMTT-V65I7P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I7P507

Extension fields and Galois Theory

B.Nithya , Dr.V. Ramadoss

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, besides understanding the roots of polynomials, Galois Theory also gave birth too 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 described 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.

Keywords

Galois Theory, group theory, roots of polynomials.

References

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Citation :

B.Nithya , Dr.V. Ramadoss, "Extension fields and Galois Theory," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 7, pp. 41-47, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I7P507