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Text: Introduction to Commutative Algebra by Atiyah-MacDonald
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):
HW1.pdfExample Sheet 1
HW2.pdfExample Sheet 2
HW3.pdfExample Sheet 3
HW4.pdfExample Sheet 4
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