Test 3
March 30, 2006
Name
Math 522
Student Number
Direction: You are required to complete this test within 1 hour and 15 minutes. In order to receive full credit, answer each problem completely and must show all work. Good Luck!
1. (15 points) Show that
Homework 10
April 13, 2006
Math 522
Direction: This homework is due on April 20, 2006. In order to receive full credit, answer each problem completely and must show all work.
1. Let F be as in Example 1 (on page 383). Use the generator z = x2 + 1 for F #
Homework 5
February 16, 2006
Math 522
Direction: This homework is due on February 23, 2006. In order to receive full credit, answer each problem completely and must show all work.
1. Consider the function : Z12 Z6 defined by (x) = x mod 6. (a) Is a ring h
Homework 4
February 09, 2006
Math 522
Direction: This homework is due on February 16, 2006. In order to receive full credit, answer each problem completely and must show all work. 1. Let R be a commutative ring with unity. Let M be an ideal of R. If R/M i
Key to Homework 1
January 12, 2006
Math 522
Direction: This homework is due on January 19, 2006. In order to receive full credit, answer each problem completely and must show all work.
1. In the ring (Z4 , +, ) solve the linear equation 2x = 2. How does y
Homework 3
January 26, 2006
Math 522
Direction: This homework is due on February 2, 2006. In order to receive full credit, answer each problem completely and must show all work.
1. Show that the principal ideal x2 + 1 generated by the element x2 + 1 of th
Homework 2
January 19, 2006
Math 522
Direction: This homework is due on January 26, 2006. In order to receive full credit, answer
each problem completely and must show all work.
1. What is the set of the units (that is, the multiplicative inverses) of the
Homework 8
March 23, 2006
Math 522
Direction: This homework is due on March 30, 2006. In order to receive full
credit, answer each problem completely and must show all work.
1. Describe the elements of Q( 3 5), where Q denotes the set of rational numbers.
Homework 7
March 10, 2006
Math 522
Direction: This homework is due on March 23, 2006. In order to receive full
credit, answer each problem completely and must show all work.
1. Let V = cfw_x R | x > 0 be the set of positive real numbers. Dene addition on
Test 1
February 2, 2006
Name Student Number
Math 522
Direction: You are required to complete this test within 1 hour and 15 minutes. In order to receive full credit, answer each problem completely and must show all work. Good Luck!
1. (15 points) If a2 =
Test 2
March 2, 2006
Math 522
Name
Student Number
Direction: You are required to complete this test within 1 hour and 15 minutes.
In order to receive full credit, answer each problem completely and must show all
work. Good Luck!
1. (15 points) Show that (
Test 4
April 20, 2006
Name
Math 522
Student Number
Direction: You are required to complete this test by Monday (April 24, 2006). In order to receive full credit, answer each problem completely and must show all work. This being a takehome test, I expect t
Homework 6
February 23, 2006
Math 522
Direction: This homework is due on (or before) March 2, 2006. In order to receive full credit, answer each problem completely and must show all work.
1. Using Eisensteins critera show that, for any prime p, the cyclot