MATH 110AH - Fall 2011
Final exam: take home part
NAME:
STUDENT ID #:
You may use the textbook and your notes.
Please work this exam on your own.
Please show all your work.
There are 5 problems for a total of 20 points.
1. (4 points) Let G be a nite group
Practice Problem Set 2 - Solution
July 28, 2015
Problem 1 Let a, b, and c be nonzero integers. Show that if c|ab and p is a prime divisor of c, then p
divides either a or b.
Solution.
Since p|c and c|ab, it is clear that p|ab. Since p is a prime number, p
Practice Problem Set 2-Ideals-solution
July 27, 2015
Problem 1 Let R be a ring, and I be an ideal of R. Prove that there is a bijection between the two sets:
cfw_J|J is an ideal of R containing I.,
cfw_J |J is an ideal of R/I..
Solution.
Let A be the form