Commutative Algebra

Homework Assignments

• due September 25:
  • [AM], p.10-15, problems 1,2,7,15-18, 27.
  • [E], p.46-56, problems 1.1, 1.2, 1.3, 1.8. 1.9, 1.13.
• due October 2:
  • [AM], p. 31-35, problems 1, 2, 4, 5, 9, 11, 12, 13-20.
• Localization. Due October 16:
  • [AM], chapter 3, p. 42-43: 1, 12, 13, 143, 21, 22, 23, 24.
  • [E], 2.4, 2.6, 2.13.
• Primary decomposition. Due November 8:
  • [AM] chapter 4, p. 55-58: 5, 7, 8, 9, 10, 13
  • [E], chapter 3: 3.3, 3.14.
• Integral closure and the Nullstellensatz. Due November 15:
  • [AM], chapter 5, p. 67-73: 2, 4, 11, 12, 13. [Note: 8, 16, 17, 18 done in class. 23, 24, 25 covered in Eisenbud]
  • [E] chapter 4 : 4.2, 4.17, 4.18, 4.20 [Note: 4,14-16 on integral closure of ideals done in [AM]
• DVRs and completions. Due: December 6:
  • [AM], chapter 1, p. 11: 5
  • [AM], chapter 7, p. 84: 2, 5
  • [AM], chapter 9, p. 99: 3, 5, 6
  • [AM] chapter 10, p. 114-115: 3, 4, 9, 10
  • [E] chapter 5, p. 155: 8 (in both examples write down the tangent cone at the origin (t=0) and explain what it is geometrically)
  • [E] chapter 7, p. 205: 1 (what is the completion of the localization?), 3.
• Dimension theory. Due December 13:
  • [AM], chapter 11, p. 125-126: 1, 2, 7 (this is [E], corollary 10.13. Do not turn in if I cover it in class)
  • [E], chapter 9, p. 230-231: 5
  • [E], chapter 10, p. 244-248: 4, 11, 12, 13 (for these last three see [AM], theorem 11.1)
  • [E], chapter 12, p. 279-284: 1, 6 (in my printing there are 2 typos on line 5 of p.281: replace R by M), 7
   

Last Updated on December 5 2000