Galois Theory

Code: MA622 | L-T-P-C: 3-0-0-6

Prerequisites: MA521 (Modern Algebra) or equivalent

Field extensions, algebraic extensions, minimal polynomials, separable and normal extensions; Automorphism groups, fixed fields, Galois extensions, Galois groups; Fundamental theorem of Galois theory, Galois closure; Galois groups of finite fields; Cyclotomic extensions, abelian extensions over rationals, Kronecker-Weber theorem; Galois groups of polynomials, symmetric functions, discriminant, Galois groups of quadratic, cubic and quartic polynomials; solvable extensions, radical extensions, solution of polynomial equations in radicals, insolvability of the quintic; cyclic extensions, Kummer theory, Artin-Schreier extensions; Galois groups over rationals, transcendental extensions, infinite Galois groups.

Texts/References:

1. D.S. Dummit and R.M. Foote, Abstract Algebra, John Wiley & Sons, Inc., II Edition, 1999.
2. I. Stewart, Galois Theory, Academic Press, 1989.
3. J.P. Escofier, Galois Theory, Springer, 2001.
4. Emil Artin, Galois Theory, University of Notre Dame Press,1971