Subsections
[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).
