ALGEBRA I
Groups: Groups, Subgroups, Normal subgroups, Quotient groups, Group homomorphisms, Isomorphisms, Isomorphism theorems, Direct products, Finitely generated abelian groups, Group actions, Permutation groups, Sylow�s theorems, Free abelian groups. Rings: Rings, Subrings, Ideals, Quotient rings, Ring homomorphisms, Integral domains, Fields, Finite fields, Polynomial rings, Simple applications to Number theory.
Modules: Modules, Submodules, Free modules, Rank of a module, Module homomorphisms.
Books
- Fraleigh, P. A.., First course in Abstract Algebra, Addison-Wesley / Narosa, 1992
- Herstein, I. N., Topics in Algebra, Vikas Publications, 1972.
- Artin, M., Algebra, Prentice_Hall of India, 1994.
- Jacobson, N., Basic Algebra � I, II, Hindustan Pub. Co., 1993.