Fall 2020 MATH GR6261 Commutative Algebra

Instructor : Eric Urban

Office hours: By zoom appointment.

Meeting time and location :

Days & Time: Tuesdays and Thursdays, 11:40pm- 12:55pm.

Location: : Online Class via zoom. Zoom link available on Courseworks

Content of the course :

- General results on rings and modules
- Noetherian and Artinian rings
- Flatness
- Primary decomposition
- Graded Rings
- Dimension and depth
- Dedekind domains
- Normal and regular rings

References :

- Introduction to Commutative Algebra by M.F. Atiyah and I.G. MacDonald

- Commutative Algebra by H Matsumura

- Alg├Ębres locales et multiplicit├ęs by J.P. Serre

Teaching Assistant :

TBA tba@math.columbia.edu

Grading policy :

Homework: 60%

Exam: 40 %

Homework : will be assigned in class every every other week and will be due a week later. Late homework will not be accepted. You are encouraged to discuss the homework with other fellow students. However, you must write up the final solutions by yourself. A Final Exam will be assigned during the week exam. from 1pm to 4pm.

Academic honesty : Copying your written work from somebody else or from any other source is considered cheating and will be dealt with severely. Permitting someone else to copy your work is also considered cheating. Any cheating during Exam or Homework will result in you failing the course.