MTH204A - Abstract Algebra

Some set theoretic notions: Relations, Functions, Partitions, Division algorithm. Various binary operations and examples. Groups and their properties, Subgroups, Cyclic groups and its subgroups, Group of integers and its properties, Fundamental theorem of arithmetic. Properties of subgroups, Lagrange theorem. Normal subgroup and Quotient group, Homomorphism, Isomorphism theorems. Symmetric group, Cyclic decomposition of a permutation, Alternating group. Group action, Class equation, Cauchy's theorem, Sylow theorems and their applications. Ring and its properties, Characteristic of a ring, Integral domain, Field, Division ring. Ideals and Quotient ring, Homomorphism, Isomorphism theorems. Polynomial ring, Unique factorization domain, Principal Ideal domain, Euclidean domain, Gaussian ring.