Basic concepts from set theory including axiom of choice, definition of groups, subgroups, Lagrange’s theorem, normal subgroups, homomorphisms, factor groups, theorems concerning homomorphisms
Group actions, Cayley’s theorem, direct and semi-direct product of groups, Orbit-stabilizer theorem, conjugacy classes and class equation, Sylow’s theorems, free groups, generators and presentation of groups.
Subnormal series, solvable groups, nilpotent groups
Definition of Rings, commutative rings, ideals, prime and maximal ideals, existence of maximal ideals, quotient construction, isomorphism theorems, ideals in polynomial rings over complex numbers and Hilbert’s nullstellensatz, fraction fields of domains
Principal ideal domains, euclidean domains, unique factorisation domains, Gauss lemma, Eisenstein criteria.
- Michael Artin, Algebra, Pearson India Education Services Pvt.Ltd
- IN Herstein, Topics in algebra, Wiley india Pvt.Ltd
- John B Fraleigh, A first course in abstract algebra, Addison-wesley
- N. Jacobson, Basic Algebra I, Dover publications
- N. Bourbaki, Algebra I, Springer-Verlag Berlin Heidelberg
- Serge Lang, Algebra, volume 211 of Graduate Texts in Mathematics, Springer-Verlag New York