Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Indian Institute of Technology Madras

Introduction to Commutative Algebra

Indian Institute of Technology Madras and NPTEL via Swayam

This course may be unavailable.


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.
INTENDED AUDIENCE : M.Sc. & Ph.D. Mathematics Students.PRE-REQUISITES : Linear Algebra, Basic group theory and Basic ring theory including ED, PID & UFD.



MODULE 1 : Rings, ring homomorphism, ideals, quotients, zero divisors, nilpotents and units.MODULE 2: Prime and maximal ideals, nilradical and Jacobsons radicalMODULE 3: Operations on ideals, extension and contraction.MODULE 4: Modules and module homomorphisms, Submodules and quotient modules, Operations on submodules, Direct sum and productMODULE 5: Finitely generated modules, Exact sequences, Tensor product of modules.MODULE 6: Restriction and extension of scalars, Exactness properties of the tensor product.MODULE 7: LocalizationMODULE 8: Integral dependence, Going-up and Going-down theorems.MODULE 9: Chain conditions, Noetherian ringsMODULE 10: Primary decomposition in Notherian rings.MODULE 11: Artinian rings



5.0 rating, based on 1 Class Central review

Start your review of Introduction to Commutative Algebra

  • Profile image for Aoi
    Covers standard topics of introductory commutative algebra. Basic knowledge of abstract algebra (ring, field, ideal) is needed to understand the topics. What I find lacking is the (geometric) motivations behind many of the technique and theorems. Overall it is a very organized and easy to follow introductory course.

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.