Commutative Algebra, Fall 2020

Lecturers:

  • Prof. Xiaojun Chen. E-mail: xjchen[at]scu[dot]edu[dot]cn.
  • Prof. Raphael Ponge. E-mail: ponge[dot]math[at]icloud[dot]com.
Prof. Chen will give lectures until November 11.

Time and Place:

Wednesdays, sections 5-7 (14:00-16:35), 3rd Teaching Building, Room 315.

References:

  • The main reference is Introduction to Commutative Algebra by M.F. Atiyah and I.G. MacDonald, Westview Press, 1969 (pdf).
  • Exercises to Atiyah and Macdonald’s Introduction to Commutative Algebra by J.D.K. Carlson (pdf). Contains all solutions of exercises in Atiyah-MacDonald’s book, as well as proofs of results omitted or left to the reader. Beware of some minor notation discrepancies with Atiyah-MacDonald’s book.

Grading Scheme:

  • You grade will be on your scores on quizzes and the final exam.
  • There will be 5 in-class quizzes throughout the semester.
  • The Final Exam will take place on December 30.

Quiz Info

  • Each quiz will consists of 2 or 3 problems from the textbook (recommended problems and/or exercises within the text).
  • Quiz 1 will take place on October 13. It will cover Chapter 1.
  • Quiz 2 will take place on November 4. It will cover Chapter 2.
  • Quiz 3 will take place on November 25. It will cover Chapter 3 and Chapter 4.
  • Quiz 4 and Quiz 5 will take place on December 16. They will cover Chapter 5.

Final Exam Info

  • The Final Exam will take place on December 30 from 14:00 to 16:40 in the usual lecture room.
  • It will cover Chapter 1 through Chapter 7 (included).

Recommended 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 [skip the Spec part], 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.

Schedule

  • Sep. 9: Chapter 1 (Rings and Ideals) (slides).
  • Sep. 16: Chapter 1 (continued).
  • Sep. 23: Chapter 1 (continued) + exercises on Chapter 1.
  • Sep. 27: Exercises on Chapter 1 + .
  • Sep. 30: Chapter 2 (Modules) (slides).
  • Oct. 7: No classes. National Day Holiday.
  • Oct. 13: Quiz 1 + Chapter 2 (continued).
  • Oct. 21: Chapter 2 (continued) + problems on Chap. 2.
  • Oct. 28: Chapter 3 (Rings and Modules of Fractions) (slides).
  • Nov. 4: Quiz 2 + Problems on Chapter 3.
  • Nov. 11: Chapter 4 (Primary Decomposition) (slides).
  • Nov. 18: Chapter 4 (continued) + Chapter 5 (Integral Dependence and Valuations) (slides).
  • Nov. 25: Quiz 3 + Chapter 5 (continued).
  • Dec. 2: Chapter 5 (continued).
  • Dec. 9: Chapter 5 (continued) + Chapter 6 (Chain Conditions) (slides) (my notes).
  • Dec. 16: Quiz 4 + Quiz 5 + Chapter 6 (continued).
  • Dec. 23: Chapter 7 (Noetherian Rings) (slides) (my notes) .
  • Dec. 30: Final Exam.