Commutative Algebra Reading Group

Text: Introduction to Commutative Algebra by Atiyah-MacDonald

We plan to meet each week on Monday's from the 23rd of February (this is the 1st week of the semester!) to 25 of May at 67-442 (this is the Priestley Building, room 442). We plan to meet from 4-6pm each week. I hope to see you all there!

Note: In the lectures, new insights, new examples and new approaches to the material is preferred. Also, its encouraged to do the mini exercises throughout the main text. Further, lecturers should give more insight were they believe the text lacks.

Exercises to do in each chapter (so far):

Chapter 1: 1, 2, 4, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 22, 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, 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

Results that are important:

• Zariski's Lemma (Proposition 7.9)

• Hilbert's Basis Theorem

• Hilbert's Nullstellensatz

• Noether Normalisation

• Direct/Inverse Limits

Additional Resources:

Cambridge Part III Commutative Algebra Examples Sheets (2021-22):