Course Details

Algebraic Extensions of Fields, Splitting Fields and Algebraic Closures, Separable and Inseparable Extensions, Cyclotomic Polynomails and Extensions, Basics of Galois theory, Fundamental Theorem and Galois Theory, Finite Fields, Composite Extensions and simple Extensions, Cyclotomic Extensions and Abelian Extensions over q, Galois Group of Polynomials, Solvable and Radical extensions, Insolvability of the quintic equations.

Course References:

1. D.S. Dummit and R.M Foote: Abstract Algebra,2nd Edition, John-Wiley, 1999.
2. S. Lang: Algebra. Revised third edition. Graudate Texts in Mathematics, 211. Springer- Verlag, New York, 2002.