Commutative Algebra Courses and Certifications

Chennai Mathematical Institute;  NPTEL

Computational Commutative Algebra

Learn computational commutative algebra through concrete Macaulay2 computations alongside foundational theory.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

NPTEL;  Chennai Mathematical Institute

Computational Commutative Algebra

This is an introductory course in computational commutative algebra. Topics in a typical first course in commutative algebra are developed along with computations in Macaulay2. The emphasis will be on concrete computations, more than on giving complete p…

• YouTube
• 1 day 7 hours
• Self-Paced
• Free Video

NPTEL;  IIT Bombay

Commutative Algebra

Explore commutative algebra through coherent core results, streamlined proofs, and the geometric viewpoint that reveals their meaning.

• YouTube
• 1 day 5 hours
• Self-Paced
• Free Video

Commutative Algebra - Primary Decomposition 2

Delve into advanced primary decomposition theory and explore noetherianity concepts in this Oxford 3rd year mathematics lecture on commutative algebra fundamentals.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Commutative Algebra - Primary Decomposition

Explore primary decomposition in commutative algebra, generalizing prime factorization from integers and polynomials to arbitrary commutative rings.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Commutative Algebra with a Viewpoint towards Algebraic Number Theory

Develop commutative algebra through integral extensions, valuation rings, discrete valuation rings, and Dedekind domains to prove class-group finiteness algebraically.

• Swayam
• Available until Oct 9, 2026
• Free Online Course

Michael Penn

Abstract Algebra - Every PID is a UFD

A proof that every principal ideal domain is a unique factorization domain, introducing ascending chain conditions and Noetherian rings.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Noether Normalization Lemma and Important Results in Dimension Theory - Tutorial 2

Explore the Noether Normalization Lemma and key results in dimension theory through detailed mathematical proofs and applications.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

NPTEL;  IISc Bangalore

Introduction to Algebraic Geometry and Commutative Algebra

An introduction to algebraic sets and the commutative algebra behind them, covering ideals, modules, localization, Zariski topology, spectra, and integral extensions.

• YouTube
• 1 day 12 hours
• Self-Paced
• Free Video

IIT Kharagpur;  NPTEL

Rings and Modules

1 rating

An elementary introduction to ring and module theory, spanning ideals, factorization, structural conditions, and tensor products.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

IIT Madras;  NPTEL

Introduction To Algebraic Geometry

Explores algebraic geometry through its interplay with commutative algebra, progressing from varieties and morphisms to schemes and their properties.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

NPTEL;  IIT Madras

Basic Algebraic Geometry - Varieties, Morphisms, Local Rings, Function Fields and Nonsingularity

Introduces algebraic geometry through varieties, morphisms, local rings, function fields, and geometric detection of smoothness.

• YouTube
• 1 day 13 hours
• Self-Paced
• Free Video

NPTEL-NOC IITM

Introduction to Algebraic Geometry

Explore fundamental concepts in algebraic geometry, from commutative algebra to schemes, covering varieties, morphisms, and sheaf theory with comprehensive tutorials.

• YouTube
• 1 day 9 hours 5 minutes
• Self-Paced
• Free Video

IIT Madras;  NPTEL

Introduction to Commutative Algebra

1 rating

Develop the core tools of commutative rings and modules: prime and maximal ideals, tensor products, localization, integral dependence, Noetherian and Artinian rings, and primary decomposition.

• Swayam
• 12 weeks
• Not Currently Offered
• Free Online Course

IISc Bangalore;  NPTEL

Introduction to Algebraic Geometry and Commutative Algebra

Builds the commutative-algebra foundations of algebraic geometry through rings, modules, localization, spectra, the Nullstellensatz, and Zariski topology.

• Swayam
• 12 weeks
• No Longer Offered
• Free Online Course