- #1

- 784

- 11

## Homework Statement

Let q be a root of p(x) = x^3 + x^2 + 1 in an extention field of Z2 (integers modulus 2). Show that Z2(q) is a splitting field of p(x by finding the other roots of p(x)

hint: this question can be greatly simplified by using the frobenius automorphism to find these zero's

## Homework Equations

frobenius automorphism : f(a) = a^p

## The Attempt at a Solution

So we are given one root and need to prove that this is enough to when adjoined to the original field to get the other two roots...

so p(q) = 0

and p(x) = (x-q)m(x) where m(x) is of degree 2

I'm a little confused on how to use the frobenius automorphism here or even why it would help at all...

anyone have any insight for me?