Syllabus: Groups: Review
of Groups, Subgroups, Homomorphisms, Normal
subgroups, Quotient groups, Isomorphism theorems.
Group actions and its applications,
Sylow theorems. Structure of finitely
generated abelian groups, Free groups. Rings: Review
of rings, Homomorphisms, Ideals and
isomorphism theorems. Prime ideals and
maximal ideals. Chinese remainder
theorem. Euclidean domains, Principal
ideal domains, Unique factorization
domains. Factorization in polynomial
rings. Modules: Modules,
Homomorphisms and exact sequences.
Free modules. Hom and tensor
products. Structure theorem for modules
over PIDs.
References:
Artin, M., Algebra, Prentice-Hall of India, 1994.
Dummit, D. S. and Foote, R. M., Abstract Algebra, John Wiley & Sons, 2001.
Hungerford, T. W., Algebra, Springer (India), 2004.
Herstein, I. N., Topics in Algebra, John Wiley & Sons, 1995.