Solution Found!

Suppose that f(x)Zp[x] and f(x) is irreducible over Zp,

Chapter 17, Problem 8E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Suppose that f(x)?Zp[x] and f(x) is irreducible over Zp, where p is a prime. If deg f(x) = n, prove that is a field with pn elements.

Questions & Answers

QUESTION:

Suppose that f(x)?Zp[x] and f(x) is irreducible over Zp, where p is a prime. If deg f(x) = n, prove that is a field with pn elements.

ANSWER:

Step 1 of 3

Implies that  is maximal ideal in , which implies that  is a field.

Now we need to count the number of elements in this field.

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back