Math 632

Math 632: Theory of Modern Algebra II --- Fall 2007

To contact the instructor: j.rhodes@uaf.edu

Course syllabus: M632syl.pdf

The dates below are when problems were assigned. Unless otherwise noted, problems are always due the following Monday.

G=Greuel and Pfister, C=Cox, Little, and O'Shea

9/7 G 1.1.1,2,4,8-12 (due 9/17); C Chapter 1, sections 1-3 (for 9/14)
9/10 a) R has 0-divisors implies R is not a field, b) R has more than 1 element implies 0 has no inverse
9/12
9/14
9/17 G 1.3.2,3,7,8,9 (misprint in 1.3.2 (1), I should be A); C Chapter 1, sections 4,5
9/19 I:J, I:J^\infty, \sqrt I are all ideals
9/21
9/24 G 1.4.1(parts 1,2,5 only),2,4,11 ; C Chapter 2, sections 1,2,3,4
9/26 For 1)A=Z/6Z ,S={1,2,4} and 2)A=Z/4Z, S={1,2,0} determine the localization of A with respect to S.
9/28
10/1 G 2.1.1,3,6,7; C Chapter 2, sections 5,6,7,8
10/3
10/5
10/8 C, Chap. 2, section 6 #2, section8 #1-4,5a,6,7a-c,8,11; G 2.1.9 (parts 1,2 only), 2.1.10, 2.1.13 ; C Chap.3, sections1,2
10/10
10/12
10/15 G 2.2.4,2.2.5; C Chap.3, sections 3,4
10/17 Complete proof of splitting of exact sequence, G 2.4.1, 2.4.6
10/19 Midterm exam out, due 10/29
10/22
10/24
10/26 Inclass Midterm
10/29 G 2.7.2,2.7.4,2.7.5; C Chap. 4, sections 1,2,3
10/31
11/2
11/5 G 3.1.1, 3.1.2(1)&(2), 3.2.1; C Chap. 4, sections 4,5,6
11/7 Does the correspondence between ideals of A containing I with ideals of A/I pair primes with primes?
11/9
11/12 Handout on minors, G 4.1.1, 4.1.2, 4.1.7; ; C Chap.5, sections 1,2,3,4
11/14
11/16 no class
11/19 G 4.1.6, 4.1.8, 4.1.12; ; C Chap.5, section 5
11/21 Deadline for project approval
11/23 Thanksgiving break
11/26
11/28
11/30