**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Categories and functors, Derived functors, Hom and functors, Flat, projective and injective modules, Resolutions of modules, Ext and Tor functors.
- Cohomology of groups.

- Recollection of rings, ideals, Spec and MaxSpec of rings, Zariski topology.
- Modules, Finitely generated modules, Nakayama lemma, Localisation of rings and modules.
- Chain conditions, Noetherian rings, Hilbert basis theorem, Artinian rings, Noetherian and Artinian modules.
- Associated primes and Primary decomposition, Integral extensions, Going up and going down theorems, Noether normalisation theorem, Hilbert Nullstellensatz and their geometric interpretations.
- Valuation rings and Dedekind domains, Ideal class group.
- Direct and inverse limits, Completions, Graded rings and modules, Artin-Rees lemma.
- Dimension theory, Hilbert and Samuel functions, Dimension theorem, Krull's principal ideal theorem.
- Regular sequences, Depth, Cohen-Macaulay rings, Gorenstein rings, Regular rings.

- Hideyuki Matsumura, Commutative Ring Theory, Cambridge Series in Advanced Mathematics 8, Cambridge University Press (1989).
- Kenneth S. Brown, Cohomology of Groups, GTM 87, Springer-Verlag (1982).
- M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Perseus Books Group (1994).
- David Eisenbud, Commutative Algebra with a view toward Algebraic Geometry, GTM 150, Springer-Verlag (1995).
- R. Y. Sharp, Steps in Commutative Algebra, Cambridge University Press (2000).