http://www.math.tamu.edu/~map/courses/627-fa06/

Homework

• HW #1: Due Wed/ 9/6
  I&R: Ch. 1: 4*, 17*, 19*, 20*

• HW #2: Due Wed. 9/20
  I&R: Ch. 1: 34, 36*, 37
  I&R: Ch. 2: 3*, 9, 10, 11*, 12*, 20, 21*
  A*: Let p, q be distinct prime numbers. Let Z[sqrt(-pq)] = { a + b*sqrt(-pq) | a, b integers }. It is straightforward to check that Z[sqrt(-pq)] is an integral domain (you should check this, but you do not need to include this argument in your solution). Show that Z[sqrt(-pq)] is not a unique factorization domain. Hint: Show that the units of Z[sqrt(-pq)] are {1, -1}, and consider the factorizations, -pq = -(p)*(q) = (sqrt(-pq))*(sqrt(-pq)).

• HW #3: Due Wed. 9/27
• HW #4: Due Fri. 10/6
• HW #5: Due Fri. 10/13
  I&R: Ch. 3: 4*, 14*, 17, 18*
  I&R: Ch. 4: 2*
  

• HW #6: Due Fri. 10/27
  I&R: Ch. 4: 6, 7*, 11, 17*, 18*, 23*
  

• HW #7: Due Fri. 11/10
  I&R: Ch. 5: 2, 3*, 4, 6*, 7, 8*, 14*, 23, 24*, 25, 29, 30*, 31
  

• HW #8: Due Mon. 11/20
  I&R: Ch. 6: 2, 4, 5*, 8*, 11*, 12, 13*, 14*, 19
  

• HW #9: Due Mon. 12/4 (not to be turned in)
  I&R: Ch. 8: 4-9, 16, 17