Introduction to Commutative Algebra 9REE8647NW
| URI | m2://res/9REE8647NW |
|---|---|
| Kind | course |
| Creators | A. V. Jayanthan (instructor) |
| Date | 2017-01-18 |
| Scope | in |
| Ids | course 03v0r5n49:111106098 |
Expressions
e1: edition
| Language | en |
|---|---|
| Date | 2017-01-18 |
- m1: page, IIT Madras (record). nptel 111106098
- m2: page, 2017-01-18 (record). nptel 111106098
Contents
- part 1: Ring theory basics
- session 1: Review of Ring Theory
- session 2: Review of Ring Theory (Ctd.)
- session 3: Ideals in commutative rings
- part 2: Ideals
- session 4: Operations on ideals
- session 5: Properties of prime ideals
- session 6: Colon and Radical of ideals
- part 3: Module theory basics
- session 7: Radicals, extension and contraction of ideals
- session 8: Modules and homomorphisms
- session 9: Isomorphism theorems and Operations on modules
- part 4: Homomorphism and Nakayama’s Lemma
- session 10: Operations on modules (Ctd.)
- session 11: Module homomorphism and determinant trick
- session 12: Nakayama’s lemma and exact sequences
- part 5: Properties of Modules
- session 13: Exact sequences (Ctd.)
- session 14: Homomorphisms and Tensor products
- session 15: Properties of tensor products
- part 6: Localization
- session 16: Properties of tensor products (Ctd.)
- session 17: Tensor product of Algebras
- session 18: Localization
- session 19: Localization (Ctd.)
- part 7: Localization and Integral dependence
- session 20: Local properties
- session 21: Further properties of localization
- session 22: Intergral dependence
- part 8: Going-up Theorem
- session 23: Integral extensions
- session 24: Lying over and Going-up theorems
- session 25: Going-down theorem
- part 9: Going-down theorem and Chain conditions
- session 26: Going-down theorem (Ctd.)
- session 27: Chain conditions
- session 28: Noetherian and Artinian modules
- session 29: Properties of Noetherian and Artinian modules, Composition Series
- part 10: Properties of Noetherian rings
- session 30: Further properties of Noetherian and Artinian modules and rings
- session 31: Hilbert basis theorem and Primary decomposition
- session 32: Primary decomposition (Ctd.)
- part 11: Primary decomposition and Artinian rings
- session 33: Uniqueness of primary decomposition
- session 34: 2nd Uniqueness theorem, Artinian rings
- session 35: Properties of Artinian rings
- part 12: Noether Normalization and Hilbert’s Nullstellensatz
- session 36: Structure Theorem of Artinian rings
- session 37: Noether Normalization
- session 38: Hilberts Nullstellensatz
- part 13: Live Session
- session 39: Live Session 02-03-2021
Catalogue records
- nptel: 111106098 (manifestation)
- nptel_video: 111106098 (manifestation)