<h3>MA7011 Advanced Topics in Commutative Algebra</h3>
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<h4>Course Details</h4>
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.
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<h4>Course References:</h4>
Text Books: <br>
1. H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1989 <br>
2. W. Bruns and J. Herzog, Cohen-Macaulay rings, Revised second edition, Cambridge University Press, 1998<br>

Reference Books:<br>
1. D. Eisenbud, Commutative Algebra with view toward Algebraic Geometry, GTM 150, Springer-Verlag, New York, 1995. <br>

2. N. Bourbaki, Elements of Mathematics - Commutative Algebra Chapters 1 - 7, Springer-Verlag, 1989. <br>