Math 5286H
Midterm 1
No collaboration is allowed. This test is open-book and open-library but no
electronic sources may be consulted.
This test is due in-class on Friday, February 12.
1. (a) Describe all possible ring homomorphisms Z[x]/(x2 + 1) Z/8.
(b)
Math 5286H
Midterm 2
No collaboration is allowed. This test is open-book and open-library but no
electronic sources may be consulted.
This test is due in-class on Friday, March 12.
1. (a) For any ring R with an ideal I
R, prove that there is a bijective
c
Math 5286H
Midterm 2 Solutions
1. (a) For any ring R with an ideal I
R, prove that there is a bijective
correspondence between maximal ideals of R/I and maximal ideals
of R that contain I .
Solution. The correspondence theorem gives a bijection between
th
Math 5286H
Midterm 1 Solutions
Note that the writeup here is somewhat terse. If you have diculty reconstructing the proof from what you see here please ask.
1. (a) Describe all possible ring homomorphisms Z[x]/(x2 + 1) Z/8.
Solution. By the universal prop
Math 5286H
Midterm 3
No collaboration is allowed. This test is open-book and open-library but no
electronic sources may be consulted.
This test is due in-class on Friday, April 9.
1. Suppose an abelian group has the presentation matrix
11 1 3
2 0 0 5
0 4
Math 5286H
Final Exam
No collaboration is allowed. This test is open-book and open-library but no
electronic sources may be consulted.
This test is due in-class on Friday, May 7.
Part A: Short answer.
Answers only, proofs are not required. (3 points each)
Math 5286H, Fundamental Structures of Algebra II
Spring 2010
Lecturer
Oce
Phone
Email
Oce hours
Course website
Tyler Lawson
Vincent Hall 323
(612) 625-6802
tlawson@math.umn.edu
Monday 11-12, Wednesday 2:30-3:30
http:/www.math.umn.edu/tlawson/5286H/
Object