PMath 334 Assignment 1 Solutions
1. Are the following subsets of C rings with the usual operations? If they are rings, are they
elds? Since they are subsets of C and we care about the usual ring opera
PMath 334 Assignment 6 Solutions - Due in class Wednesday, June 27, 2012. Hand in solutions
to the following problems. Be sure to justify your answers and neatly present your work.
1. Let R be a ring
PMath 334 Assignment 5 Solutions.
1. Find the (monic) gcd of f (x) and g (x) in k [x] and write it as uf + vg . Is f a unit of k [x]/(g )?
If so, what is its multiplicative inverse?
(a) f = x2 5, g =
PMath 334 Assignment 4 - Solutions
Neatly present your work and justify your answers for the following problems.
1. Let R be a ring and let b R. We say that b is idempotent if b2 = b. For example, 0 a
PMath 334 Assignment 2 - Due in class Wednesday, May 23, 2012.
Hand in solutions to the following problems - be sure to neatly present your work and to justify
your answers.
1. The ring Z4 does not co
PMath 334 Assignment 3 Solutions - Due in class Wednesday, May 30, 2012.
Neatly present your work and justify your answers for the following problems.
1. Find all of the ideals of Z12 . For each ideal
PMath 334 Assignment 7 Solutions. Hand in solutions to the following problems. Be sure to
justify your answers and neatly present your work.
1. Let = 2+ 2i C. Find the minimal polynomial of over the f
PMath 334 Assignment 8 Solutions - Due in class Wednesday, July 18, 2012. Hand in solutions
to the following problems. Be sure to justify your answers and neatly present your work.
1. Let R be an inte
PMath 334 Quiz 3 Solutions - Friday, May 25, 2012
Write your name and ID number somewhere at the top of the page. Justify all of your answers. Each of the three questions are of equal value.
1. The th
PMath 334 Quiz 4 - Friday, June 1, 2012
Write your name and ID number somewhere at the top of the page. Justify all of your answers. Each of the two questions are of equal value.
1. Prove that R[x]/(x
PMath 334 Quiz 2 - Friday, May 18, 2012
Write your name and ID number somewhere at the top of the page. Each of the three questions
are of equal value.
1. Let C satisfy 2 = + 3. Consider the function
PMath 334 Quiz 1 Solutions
Write your name and ID number somewhere at the top of the page.
1. True or False? Just say your answer, no need to justify anything!
(a) [6] is a unit of Z15 . Answer: False
PMath 334 Assignment 9 - Not due at all, but good practice. These are not neccesarily in order
of increasing diculty.
1. (In honour of the last quiz question which was poorly stated, but not poorly st
PMath 334 Midterm Test Solutions - Monday, June 11, 2012. By a ring I mean a commuting
ring where 0 = 1. All homomorphisms send 1 to 1.
1. Yes or no? Just write down your answer in your booklet!
[2](a