Computational Commutative Algebra
Chennai Mathematical Institute and NPTEL via Swayam
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Overview
INTENDED AUDIENCE :Advanced undergraduate / post-graduate studentsPREREQUISITES :Introduction to basic theory of rings, modulesINDUSTRIES SUPPORT :None
Syllabus
COURSE LAYOUT
Week 1:Introduction: rings and ideals, ring homomorphisms, Hilbert basis theorem, Hilbert Nullstellensatz, introduction to Macaulay2Week 2:Groebner bases, ideal membership, solving systems of polynomial ringsWeek 3:Modules.Week 4:Associated primes and primary decompositionWeek 5:Associated primes and primary decomposition, ctd.Week 6:Integral extensions, integral closure, Noether normalizationWeek 7:Integral extensions, integral closure, Noether normalization, ctd.Week 8:Hilbert functions, dimension theory
Week 9:Hilbert functions, dimension theory ctd.Week 10:Applications to geometry.Week 11:Homological algebra: depth, Koszul complexWeek 12:Homological algebra: free resolutions, Auslander-Buchsbaum formula
Taught by
Prof. Manoj Kummini
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