Homework Assignments in Commutative Algebra

Math 351, Spring 2010

Professor Sands: sands@cems.uvm.edu

Office Hours: M 12:15-1:15, Tu 1-2, W 3:30-4:30, F 12-12:30
Room 404, 16 Colchester Ave. 656-4339
Syllabus

All problems are in "Introduction to Commutative Algebra" by M.F. Atiyah and I.G. MacDonald
 If you have questions, you can contact me using email: sands@cems.uvm.edu

#      Due            Homework                                               Topic
 
  1  Jan. 25 Chap. 1 #1,3
 Rings and Ideals
 2 Feb. 1 Chap. 1 # 18,19,21,26,(27),28
 Prime Spectrum of a Ring
 3 Feb 8. Chap. 2 # 10,12,15,18,21
 Modules
 4 Feb. 17
 Chap. 2 # 1,7,8a,11
 Tensor Products
 5 Feb. 22
 Chap. 3 #1, 3, 5, 12
 Localization
 6  Mar. 1
 Chap. 4 # 2, 4, 5, 7i, 7ii, 8
 Primary Decomposition
 7 Mar. 15
 Chap. 5  # 6, 12, 18
 Integral Extensions and Valuations
 8 Mar. 22 Chap. 5. # 27, 30
Chap. 6 # 1, 4
 Continued
Chain Conditions
 9 Mar. 29
 Chap. 7  #2, 7, 8
 Noetherian Rings
 10 Apr. 5
  Chap. 8 # 3,6
 Artinian Rings
 11 Apr. 12 
Chap. 9 # 4, 7 9
 Discrete Valuations and Dedekind Domains
 12 Apr. 19
 Chap. 10 # 1, 2, 6
 Completion
13 Apr. 26
 Chap. 11 # 6 (first inequality)
 Dimension Theory
14
 May 10
 Final Assignment to be handed out
 Review