Math 621
Algebra I
Spring 2015
Problem Sets

Problem Set Mash #3: Due on Wednesday May 6 (last day of class). Problem Set Mashes must be typed. I will accept this Mash up to one day late electronically, with no penalty.
Turn in Questions 1-4 from Problem Set #10
and Dummit and Foot 8.3 #1

Problem Set #11. Due Wednesday May 6
Section 9.1 # 5, 8
Section 9.2 #3, 7
Problem Set #10. Due Thursday April 30
1. Let Z be the set of integers. Prove that the map Z[3i] --> Z defined by a+3bi --> a is NOT a homomorphism of rings.
2. Show that the same map Z[3i] --> Z/9Z is a homomorphism. Use the First Isom. Theorem to make a conclusion.
3. Why does your conclusion in #2 imply that 3i is irreducible but not prime in Z[3i]?
4. Prove that Z[i] is a unique factorization domain.

8.3 # 5, 6
9.1 #1, 2, 4


Problem Set #9. Due Thursday April 23.
Dummit and Foot
Section 7.5 #3
Section 7.6 #5
Section 8.1 #1(c), 2(b), 6, 7
Section 8.2  #1, 3, 5
Section 8.3 #1, 4


Problem Set Mash #2:  Due on  April  7. Problem Set Mashes must be typed. No late Mashes will be accepted.

Problem Set #8. Due Tuesday April 15.
Dummit and Foot
Section 7.2 #1, 3, 4
Section 7.3 #2, 6, 10, 11
Section 7.4 #1, 4, 5

Problem Set #7. Due Tuesday April 8.
Dummit and Foote
Section 4.4 #1, 2
Section 4.5 #17, 22
Section 5.1 #4
Section 5.2 #1,4
Section 7.1 #6, 13, 26

Mash #2 Due April 8.
Dummit and Foote
Section 3.3 #6, 8
Section 3.5 #11
Section 4.2 #2, 4
Section 4.5 #17
Section 5.1 #4

Problem Set #6. Due Thursday March 19.
Dummit and Foote
Section 3.3 #3, 4, 6, 8
Section 3.5: #1, 3, 7, 11
Section 4.1: #1, 2, 4
Section 4.2: # 1, 2, 4

Problem Set #5. Due Thursday February 26.
 Dummit and Foote
Section 3.1, #1, 2, 3, 10, 14, 19, 33
Section 3.2 # 1, 4, 5, 8

Mash #1 Due February 26: Mash #1 Solution Set, by Ryan Vaughn (checked for accuracy by R. Goldin). Please let me know if you have any concerns or questions about the solutions.

Section 1.2 #15
Section 1.4 #10
Section 1.6 #9, 18
Section 1.7 #4
Section 2.1 #10
Section 2.2 #6 
Section 2.3 #16
Section 2.4 #7, 11
Please Latex your solutions. If you are new to latex, please latex at least three problems and turn the others in using another form of neat writing.
Problem Set #1. Due Tuesday January 27.
Dummit and Foote
Section 1.1 #4, #6, #13, #22
Section 1.2 #3, #15
Section 1.3 #4a, #5, #11
Section 1.4 #3, #10

Problem Set #2. Due Tuesday February 3.
Dummit and Foote
Section 1.3 #10, #14, #15
Section 1.6 #1(a,b), #3, #4, #9, #13, #18, #20

Problem Set #3. Due Tuesday February 10.
Dummit and Foote
Section 1.6 #22, #25
Section 1.7 #2, #3, #4, #10
Section 2.1 #1, #2, #4, #10

Problem Set #4. Due Tuesday February 17.
Dummit and Foote
Section 2.2 #4, #6, #11, #12c,d
Section 2.3 #8, #12, #16, #21
Section 2.4 #2, #3, #7, #11