NPTEL : NOC:Computational Commutative Algebra (Mathematics)

Co-ordinators : Prof. Manoj Kummini


Lecture 1 - Definitions

Lecture 2 - Homomorphisms

Lecture 3 - Quotient rings

Lecture 4 - Noetherian rings

Lecture 5 - Monomials

Lecture 6 - Initial ideals

Lecture 7 - Division algorithm

Lecture 8 - Grobner basis

Lecture 9 - Solving Polynomial Equations

Lecture 10 - Nullstellensatz - Part 1

Lecture 11 - Nullstellensatz - Part 2

Lecture 12 - Buchberger criterion

Lecture 13 - Monomial basis

Lecture 14 - Elimination

Lecture 15 - Modules - Part 1

Lecture 16 - Modules - Part 2

Lecture 17 - Localisation

Lecture 18 - Nakayama Lemma

Lecture 19 - Spectrum - Part 1

Lecture 20 - Spectrum - Part 2

Lecture 21 - Associated primes

Lecture 22 - Primary Decomposition

Lecture 23 - Support of a module

Lecture 24 - Associated primes

Lecture 25 - Prime avoidance

Lecture 26 - Saturation - Part 1

Lecture 27 - Saturation - Part 2

Lecture 28 - Saturation - Part 3

Lecture 29 - Morphisms - Part 1

Lecture 30 - Morphisms - Part 2

Lecture 31 - Integral extensions

Lecture 32 - Noether normalisation lemma

Lecture 33 - Noether normalisation lemma

Lecture 34 - Polynomial rings

Lecture 35 - Going up theorem

Lecture 36 - Artinian rings

Lecture 37 - Graded modules

Lecture 38 - Hilbert polynomial

Lecture 39 - Hilbert-Samuel polynomial

Lecture 40 - Artin Rees Lemma

Lecture 41 - Degree of Hilbert-Samuel polynomial

Lecture 42 - Dimension of noetherian local rings - Part 1

Lecture 43 - Dimension of noetherian local rings - Part 2

Lecture 44 - Dimension of polynomial rings

Lecture 45 - Algebras over a field

Lecture 46 - Graded rings - Part 1

Lecture 47 - Graded rings - Part 2

Lecture 48 - Polynomial rings over fields

Lecture 49 - Hilbert series - Part 1

Lecture 50 - Hilbert series - Part 2

Lecture 51 - Proj of a graded ring

Lecture 52 - Homogenization - Part 1

Lecture 53 - Homogenization - Part 2

Lecture 54 - More on graded rings

Lecture 55 - Free resolutions

Lecture 56 - Computing syzygies

Lecture 57 - Koszul complex

Lecture 58 - More on Koszul complexes

Lecture 59 - Castelnuovo Mumford regularity

Lecture 60 - Castelnuovo Mumford regularity