Commutative Algebra

Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings, rings of algebraic integers, including the ordinary integers , and p-adic integers. Commutative algebra is the main technical tool in the local study of schemes in algebraic geometry.

Classroom: 2-143

Time: Tu/Th 13-14:30

Email: cyxu [ at ] math.mit.edu

Textbook:  Atiyah, M. F.; Macdonald, I. G. Introduction to commutative algebra.

Score: 40% Problem set 30% Midterm 30% Final report

Office hour: Th 14:30-16:30

Tentative Schedule:

Nov. 6 Midterm 

Problem sets: 

Chapter 1: 1-5, 10, 12-14

Chapter 1: 15-21, 27, 28

Other references: