Commutative Algebra, Fall 2022

Lecturer:

  • Prof. Raphael Ponge.
  • E-mail: ponge[dot]math[at]icloud[dot]com.

Time and Location:

  • Mondays from 8:00-9:40, 3rd Teaching Building, Room 107.
  • Until further notice the lectures will be online. Here is the Tencent Meeting link. Meeting ID: 617-4920-0040.
  • The lectures are from Week 2 through Week 18. The last class is on December 26, 2022.

Main Reference:

  • Introduction to Commutative Algebra by M.F. Atiyah and I.G. MacDonald, Westview Press, 1969 (pdf).

Further Reading:

  • Exercises to Atiyah and Macdonald’s Introduction to Commutative Algebra by J.D.K. Carlson (pdf). These notes contain all solutions to the exercises in Atiyah-MacDonald’s book. They also contain proofs of results omitted or left to the reader in Atiyah-MacDonald’s book. Beware of some minor notation discrepancies with Atiyah-MacDonald’s book.
  • About Atiyah and MacDonald’s book by P.Y. Gaillard (pdf). These notes also contain solutions to the exercises in Atiyah-MacDonald. There are some useful additional comments on the main results in Atiyah-MacDonald’s book.
  • A Term of Commutative Algebra by A. Altman and S. Kleiman, Worldwide Center of Mathematics, 2017 (pdf). A modernized version of Atiyah-MacDonald’s book. Contains details that are not contained in MacDonald’s book or Carlson’s notes.

Grading Scheme:

Your grade will be based on your scores on the quizzes and the Final Exam. There will be 5 in-class quizzes throughout the semester.

Quiz Info:

  • Each quiz will consists of 2~4 problems from the textbook (selected problems and/or exercises within the text).

Selected Problems:

  • Chapter 1: #1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 22 (1st part only), 26, 28.
  • Chapter 2: #1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.
  • Chapter 3: # 1, 2, 3, 4, 5, 6, 7, 8, 9, 12[(i), (ii), (iii) only], 13, 14, 15.
  • Chapter 4: # 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16.
  • Chapter 5: #1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14.
  • Chapter 6: # 1, 2, 3, 4, 5, 6.
  • Chapter 7: # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
  • Chapter 8: # 1, 2, 3, 6.

Schedule:

  • Sep. 5: Chapter 1 (Rings and Ideals) (slides).
  • Sep. 12: No classes, Mid-Autumn Festival.
  • Sep. 19: Chapter 1 (continued) + Chapter 2 (Modules).
  • Sep. 26: Chapter 2 (continued).
  • Oct. 4: No classes, National Day Holiday.
  • Oct. 11: Chapter 2 (continued).
  • Oct. 18: Chapter 3 (Rings and Modules of Fractions).