MA7011 Advanced Topics in Commutative Algebra

Course Details

Review of commutative rings, ideals and modules. Localisation and Spectrum of a ring, Nullstellensatz, Dimension theory, Associated primes and primary decomposition, Flatness, Completion and Artin-Rees lemma, Integral extensions, Graded rings, The Hilbert and Samuel functions, system of parameters and multiplicity, Regular sequences and Koszul complex, Cohen-Macaulay rings and Gorenstein rings, Regular rings, UFDs and Complete intersections.

Course References:

Text Books:
1. H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1989
2. W. Bruns and J. Herzog, Cohen-Macaulay rings, Revised second edition, Cambridge University Press, 1998
Reference Books:
1. D. Eisenbud, Commutative Algebra with view toward Algebraic Geometry, GTM 150, Springer-Verlag, New York, 1995.
2. N. Bourbaki, Elements of Mathematics - Commutative Algebra Chapters 1 - 7, Springer-Verlag, 1989.