Introduction to Commutative Algebra

By Prof. A. V. Jayanthan | IIT Madras

Learners enrolled: 499

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.

Summary

Course Status :	Completed
Course Type :	Elective
Language for course content :	English
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Postgraduate
Start Date :	18 Jan 2021
End Date :	09 Apr 2021
Enrollment Ends :	01 Feb 2021
Exam Date :	24 Apr 2021 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

MODULE 1 : Rings, ring homomorphism, ideals, quotients, zero divisors, nilpotents and units.

MODULE 2: Prime and maximal ideals, nilradical and Jacobsons radical

MODULE 3: Operations on ideals, extension and contraction.

MODULE 4: Modules and module homomorphisms, Submodules and quotient modules, Operations on submodules, Direct sum and product

MODULE 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: Localization

MODULE 8: Integral dependence, Going-up and Going-down theorems.

MODULE 9: Chain conditions, Noetherian rings

MODULE 10: Primary decomposition in Notherian rings.

MODULE 11: Artinian rings

Books and references

None

Instructor bio

Prof. A. V. Jayanthan

IIT Madras

Professor at IIT Madras Mathematic Department. Profile: https://home.iitm.ac.in/jayanav/

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 24 April 2021 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

SWAYAM Helpline / Support