Learn · Computational Commutative Algebra
Lecture 5 of 60Week 1
Monomials
Prof. Manoj Kummini · Chennai Mathematical Institute
Credits and licence
- From
- Computational Commutative Algebra, Chennai Mathematical Institute (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Definitions
- Homomorphisms
- Quotient rings
- Noetherian rings
- Monomials
- Initial ideals
- Division algorithm
- Grobner basis
- Solving Polynomial Equations
- Nullstellensatz - Part 1
- Nullstellensatz - Part 2
- Buchberger criterion
- Monomial basis
- Elimination
- Modules - Part 1
- Modules - Part 2
- Localisation
- Nakayama Lemma
- Spectrum - Part 1
- Spectrum - Part 2
- Associated primes
- Primary Decomposition
- Support of a module
- Associated primes
- Prime avoidance
- Saturation - Part 1
- saturation - Part 2
- saturation - Part 3
- Morphisms - Part 1
- Morphisms - Part 2
- Integral extensions
- Noether normalisation lemma
- Noether normalisation lemma
- Polynomial rings
- Going up theorem
- Artinian rings
- Graded modules
- Hilbert polynomial
- Hilbert-Samuel polynomial
- Artin Rees Lemma
- Degree of Hilbert-Samuel polynomial
- Dimension of noetherian local rings - Part 1
- Dimension of noetherian local rings - Part 2
- Dimension of polynomial rings
- Algebras over a field
- Graded rings - Part 1
- Graded rings - Part 2
- Polynomial rings over fields
- Hilbert series - Part 1
- Hilbert series - Part 2
- Proj of a graded ring
- Homogenization - Part 1
- Homogenization - Part 2
- More on graded rings
- Free resolutions
- Computing syzygies
- Koszul complex
- More on Koszul complexes
- Castelnuovo Mumford regularity
- Castelnuovo Mumford regularity