Notes on A&M’s Exercises
This document provides a series of solutions to selected exercises from the classic introductory textbook Introduction to Commutative Algebra by M. F. Atiyah and I. G. Macdonald. For more information about this book, refer to the Google Books link.
Chapter 1
Exercise 1.1 [Link]
Exercise 1.2(i) [Link]
Exercise 1.2(ii) [Link]
Exercise 1.3(i) [Link]
Exercise 1.4 [Link]
Exercise 1.5(i) [Link]
Exercise 1.6 [Link]
Exercise 1.7 [Link]
Exercise 1.8: Refer to the solution of Exercise 1.1.5 in Matsumura for a stronger result. [Link]
Exercise 1.9 [Link]
Exercise 1.10 [Link]
Exercise 1.11 [Link]
Exercise 1.12 [Link]
Exercise 1.22 [Link]
Chapter 2
Exercise 2.1 [Link]
Exercise 2.2 [Link]
Chapter 3
Exercise 3.7 [Link]
Chapter 4
Exercise 4.2 [Link]
Chapter 5
Exercise 5.28 [Link]
Chapter 6
Exercise 6.2 [Link]
Exercise 6.3 [Link]
Notes on Matsumura’s Exercises
This is a series of solutions to selected exercises from Hideyuki Matsumura's book Commutative Ring Theory. Refer to the Google Books link for more information about this book. In each note, I will briefly introduce the background of the target exercise, recall and assume some useful results, and provide detailed proof of the exercise. As a preparation for algebraic geometry and advanced topics in commutative algebra (e.g., topics in Cohen--Macaulay ring theory), this book offers a solid and comprehensive foundation for graduate or advanced undergraduate students.
Chapter 1
Exercise 1.1.2 [Link]
Exercise 1.1.5 [Link]
Exercise 1.3.1 [Link]
Exercise 1.3.3 [Link]
Exercise 1.3.6 [Link]
Chapter 2
Exercise 2.4.6: Refer to the solution of Exercise 1.22 in A&M for a stronger result. [Link]
Exercise 2.4.7: Refer to the solution of Exercise 1.22 in A&M for a stronger result. [Link]
Note Series: Completion of Rings
The notes in this series focus on the theory and applications of ring completions.
Note 1: Topological Abelian Groups [Link]
Note 2: Topological Rings and Modules [Link]