# MA2ALA Coursework

This Assessment should be submitted online via BLACKBOARD (via the submission point in the
on paper and then upload a scan of your work in the form of a single PDF file. The marks
available for each question are shown on the right hand side of the page. The maximum mark
possible is 40. The assessment will count for 10% of your final MA2ALA mark.

1. (a) Classify all non-zero elements of Z15 into units and zero divisors.
4 marks
(b) Pick any unit [u] that is not [1] or [14] and find n such that [u]
n = [1].
2 marks
(c) For the element chosen in part (b), find the inverse.
1 mark
(d) Does the equation [5]x = [0] have any non-zero solutions? If no, why not? If yes, list
all solutions.
3 marks
2. Use Noether’s Isomorphism Theorem to show Z30/(5) ∼= Z5.
10 marks
3. (a) For each pair of polynomials f, g ∈ Q[x], find the greatest common divisor.
(i) f = x
5 + 2x
4 − x
2 + 1, g = x
4 + 1;
(ii) f = 2x
5 + 2x
3
, g = 2x
3 − 2x
2 + 2x − 2.
4 marks
(b) For each pair of polynomials in part (a), find a polynomial p(x) ∈ F[x] such that
(f, g) = (p).
2 marks
(c) For each pair of polynomials in part (a), decide if the ideal (f, g) is prime. Justify
1
4 marks
4. (a) Compute the minimal polynomial of α =

3 + √
6 marks
(b) Consider the polynomial,
f(x) = x
35 − 12x
26 − 9x
24 + 39x
16 + 21x
11 − 27x
4 + 3x + 6.
Let β denote one of the roots of f(x) in C, and let K = Q(β). Give a basis for K as
4 marks
2
Pages (550 words)
Approximate price: -

## Reasons to trust Research Paper 101

On Time Delivery

We pride ourselves in meeting the deadlines of our customers. We take your order, assign a writer but allow some more time for ourselves to edit the paper before delivering to you. You are guaranteed a flawless paper on a timely manner...

24x7 Customer Live Support

Our team at Research Paper 101 is committed to handling your paper according to the specfications and are available 24*7 for communication. Whenever you need a quick help, you can talk to our writers via the system messaging or contact support via live chat and we will deliver your message instantly.

Experienced Subject Experts

Online Experts from Research Paper 101 are qualified both academically and in their experiences. Many are Masters and Phd holders and therefore, are qualified to handle complex assignments that require critical thinking and analyses...

Customer Satisfaction

We offer dissertation papers as per students’ wishes. We also help craft out the best topics and design concept papers. By ordering with us, you are guaranteed of defending and making through those hard faced professors in the defense panel!

100% Plagiarism Free

We at Research Paper 101 take plagiarism as a serious offence. From the start, we train our writers to write all their papers from scratch. We also check if the papers have been cited appropriately. Our website also has a tool designed to check for plagiarism that has been made erroniusly. In essense, the paper you get will be 100% legit...

Affordable Prices

We understand that being a student is very challenging, some students balance between work and studies in order to survive. We therefore offer pocket friendly rates that are very competitive in the market.

Try it now!

## Calculate the price of your order

Total price:
\$0.00

How it works?

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

## Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.