MATH W4041:
Intro to Modern Algebra I
Spring 2010
Exam
Our second midterm will be held in class on November 16.
| Test |
Day |
Date |
Time |
Points |
| Exam 2 | Tuesday | November 16 | in class | 30 |
Problem Session
| Day |
Date |
Time |
Place |
| Wednesday |
November 10 |
7:30 pm |
507 Math |
"The Universe"
For the exam, you are responsible for the following topics:
-
Define unit, associate, proper divisor, irreducible, prime. Where possible, give a second definition in terms of ideals.
-
Define and give examples of a Principal Ideal Domain, Unique Factorization Domain, Euclidean Domain.
-
State and prove Gauss's lemma.
-
Prove that the Gaussian integers are a Euclidean Domain. List its first few primes.
-
Prove that for a Principal Ideal Domain, any infinite ascending chain stabilizes.
-
State and prove the Eisenstein criterion, and be able to apply it.
-
Diagonalize an integer matrix using row and column operations.
-
Given an abelian group described by generators and relations, express G as a product of free and cyclic groups.
-
Unmask the identity of the Doodle poll participant "The Ring Leader."