This page contains information about the course MT3114 Rings and Module that I am teaching in the semester August-December 2022 in IISER Pune.

Schedule :

Evaluation :

• Assignments and/ or Quiz 30%

• Mid Sem 30%

• End Sem 40%

Syllabus:

• Rings, Ideals (Prime Ideals, Maximal Ideals), Quotient Rings, Homomorphism of Rings

• Chinese Reminder Theorem, Isomorphism theorems

• Factorization Domains (PID, ED, UFD)

• Modules over a commutative rings

• Submodules, Quotient Modules, Direct sum

• Homomorphisms of Modules, Isomorphism Theorems

• Free Modules, Structure theorem of modules over a PID

• Canonical Forms (Jordan and Rational)

• Localization of Rings and Modules

• Tensor Product of Modules

Lecture Notes:

Assignment: Assignment 1

Assignment 3

Assignment 4

References:

• Abstract Algebra- Dummit and Foote

• Introduction to Rings and Modules - C. Musili

• Contemporary Abstract Algebra- J. A. Gallian