Course No
M307
Credit
4
Syllabus
Field extensions, algebraic extensions, Ruler and compass constructions, splitting fields, algebraic closures, separable and inseparable extensions, cyclotomic polynomials and extensions, automorphism groups and fixed fields, Galois extensions, Fundamental theorem of Galois theory, Fundamental theorem of algebra, Finite fields, Galois group of polynomials, Computations of Galois groups over rationals, Solvable groups, nilpotent groups, Solvability by radicals, Transcendental extensions.
Text Books
- D. S. Dummit, R. M. Foote, “Abstract Algebra”, Wiley-India edition, 2013.
Reference Books
I. N. Herstein, “Topics in Algebra”, Wiley-India edition, 2013.M. Artin, “Algebra”, Prentice-Hall of India, 2007.J. Rotman, “Galois Theory”, Universitext, Springer-Verlag, 1998.