Course: MAT 375 3.0 Ring Theory (Compulsory)
Course Content: Definitions and Examples, Some Simple Results, Ideals, Homomorphisms (as a generalization of Homomorphism Theorems in groups), Quotient Rings, Integral Domains, Ideals and Factor Rings, Homomorphisms, Isomorphism Theorems, Maximal ideals, Prime ideals/rings and applications. Factorization in Commutative Rings (Prime elements, irreducible elements, unique factorization domains, Euclidean domains ). Local rings, Rings of Polynomials and formal Power series, Factorization in Polynomial Rings. Chain Conditions & Rings of quotients and Localization.
Recommend Readings: Algebra,Thomas W.Hungerford, A First Course In Abstract Algebra,John B.Fraleig