Introduction to Commutative Algebra

COURSE LAYOUT

MODULE 1 : Rings, ring homomorphism, ideals, quotients, zero divisors, nilpotents and units.

MODULE 2: Prime and maximal ideals, nilradical and Jacobsons radical

MODULE 3: Operations on ideals, extension and contraction.

MODULE 4: Modules and module homomorphisms, Submodules and quotient modules, Operations on submodules, Direct sum and product

MODULE 5: Finitely generated modules, Exact sequences, Tensor product of modules.

MODULE 6: Restriction and extension of scalars, Exactness properties of the tensor product.

MODULE 7: Localization

MODULE 8: Integral dependence, Going-up and Going-down theorems

.MODULE 9: Chain conditions, Noetherian rings

MODULE 10: Primary decomposition in Notherian rings.

MODULE 11: Artinian rings