Rings, ideals, quotient rings, ring homomorphisms, isomorphism theorems, prime ideals, maximal ideals, Chinese remainder theorem, Field of fractions, Euclidean Domains, Principal Ideal Domains, Unique Factorization Domains, Polynomial rings, Gauss lemma, irreducibility criteria.
Modules, submodules, quotients modules, module homomorphisms, isomorphism theorems, generators, direct product and direct sum of modules, free modules, finitely generated modules over a PID, Structure theorem for finitely generated abelian groups, Rational form and Jordan form of a matrix, Tensor product of modules.
- D. S. Dummit, R. M. Foote, “Abstract Algebra”, Wiley-India edition, 2013.
- I. N. Herstein, “Topics in Algebra”, Wiley-India edition, 2013.
- M. Artin, “Algebra”, Prentice-Hall of India, 2007.