COMMUTATIVE ALGEBRA
Noetherian rings and Modules, Localisations, Exact Sequences, Hom, Tensor Products, Hilbert’s Null-stellensatz,
Integral dependence, Going-up and Going down theorems, Noether’s normalization lemma , Discrete valuation
rings and Dedekind domains.
Books
- Atiyah, M. F. and Macdonald, I.G., Introduction to Commutative Algebra, Addison-Wesley, 1969.
- Raghavan.,S. B.., Singh and Sridharan, R., Homological Methods in Commutative Algebra, TIFR Mathematical Pamphlet Number 5, Oxford University Press, 1977.
- Serre, J. P., Local Algebra (translated from French), Springer Monographs in Mathematics, Springer-Verlag, 2000.
- Zariski, O and Samuel, P., Commutative Algebra, Vols.I and II, Van Nostrand, 1958 and 1960.