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Last updated:

September 23, 2023

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

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Unlimited Duration

Description

Introduction to Commutative Algebra. Instructor: Prof. A. V. Jayanthan, Department of Mathematics, IIT Madras.

This is an introductory course in Commutative Algebra where most basic tools on commutative rings and modules over commutative rings are developed. This course is essential for anyone who wants to do research in areas such as commutative algebra, algebraic geometry, algebraic number theory etc. (from nptel.ac.in)

Course Curriculum

    • Lecture 01 – Review of Ring Theory Unlimited
    • Lecture 02 – Review of Ring Theory (cont.) Unlimited
    • Lecture 03 – Ideals in Commutative Rings Unlimited
    • Lecture 04 – Operations on Ideals Unlimited
    • Lecture 05 – Properties of Prime Ideals Unlimited
    • Lecture 06 – Colon and Radical of Ideals Unlimited
    • Lecture 07 – Radicals, Extension and Contraction of Ideals Unlimited
    • Lecture 08 – Modules and Homomorphisms Unlimited
    • Lecture 09 – Isomorphism Theorems and Operations on Modules Unlimited
    • Lecture 10 – Operations on Modules (cont.) Unlimited
    • Lecture 11 – Module Homomorphism and Determinant Trick Unlimited
    • Lecture 12 – Nakayama’s Lemma and Exact Sequences Unlimited
    • Lecture 13 – Exact Sequences (cont.) Unlimited
    • Lecture 14 – Homomorphisms and Tensor Products Unlimited
    • Lecture 15 – Properties of Tensor Products Unlimited
    • Lecture 16 – Properties of Tensor Products (cont.) Unlimited
    • Lecture 17 – Tensor Product of Algebras Unlimited
    • Lecture 18 – Localization Unlimited
    • Lecture 19 – Localization (cont.) Unlimited
    • Lecture 20 – Local Properties Unlimited
    • Lecture 21 – Further Properties of Localization Unlimited
    • Lecture 22 – Integral Dependence Unlimited
    • Lecture 23 – Integral Extensions Unlimited
    • Lecture 24 – Lying Over and Going-up Theorems Unlimited
    • Lecture 25 – Going-down Theorem Unlimited
    • Lecture 26 – Going-down Theorem (cont.) Unlimited
    • Lecture 27 – Chain Conditions Unlimited
    • Lecture 28 – Noetherian and Artinian Modules Unlimited
    • Lecture 29 – Properties of Noetherian and Artinian Modules, Composition Series Unlimited
    • Lecture 30 – Further Properties of Noetherian and Artinian Modules and Rings Unlimited
    • Lecture 31 – Hilbert Basis Theorem and Primary Decomposition Unlimited
    • Lecture 32 – Primary Decomposition (cont.) Unlimited
    • Lecture 33 – Uniqueness of Primary Decomposition Unlimited
    • Lecture 34 – 2nd Uniqueness Theorem, Artinian Rings Unlimited
    • Lecture 35 – Properties of Artinian Rings Unlimited
    • Lecture 36 – Structure Theorem of Artinian Rings Unlimited
    • Lecture 37 – Noether Normalization Unlimited
    • Lecture 38 – Hilbert’s Nullstellensatz Unlimited

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