Rings and Fields: U.F.D., P.I.D, factorization of polynomials. Field extensions. Normal extensions, Separable extensions. Galois extensions, Galois group. Fundamental theorem of Galois Theory. Cyclic Extensions, Solvability by radicals. Geometric constructions.
Groups: Solvable and nilpotent groups. Presentation of groups. Fundamental theorem for finitely generated Abelian groups. Semi-direct products, amalgamated products and HNN- extensions.
Prerequisite(s): Algebra 1.
- M. Artin: Algebra, Second Edition, Pearson Prentice-Hall of India, New Delhi, 2011.
- D. S. Dummit and Richard M. Foote: Abstract Algebra, Third Edition, Wiley, 2005.
- Patrick Morandi: Field and Galois Theory. Springer, 1996.
- Yvette Kosmann-Schwarzbach: Groups and Symmetries: From Finite Groups to Lie Groups. Springer, 2010.
- I. S. Luthar and I. B. S. Passi: Algebra Vols I & 2, Narosa, 1996, 1999.