MA6470       COMMUTATIVE ALGEBRA

Rings and Modules, Localisation of Rings and Modules, Noetherian Rings and Modules, Primary Decomposition, Artinian rings, Integral Extensions, Going-up, Lying-over and Going-down Theorems, Hilbert's Nullstellensatz, Noether's Normalisation, Dimension Theorem, Krull's Principal Ideal Theorem, Dedekind Domains.

Books:

1.M. F. Atiyah and I. G. Macdonald: Introduction to Commutative Algebra, Addision-Wesley , 1969.

2.N. S. Gopalakrishnan: Commutative Algebra, Oxonian Press, 1984.