I understand what you're doing there.
Two more things:
How do I prove that this a homomorphism?
Also, wouldn't 0 also be in the kernel? Is this allowed for the First Isomorphism Theorem?
First, I apologize, I meant to right that the polynomial being modded out of Q[x] is x^2 - 3, not x^3 - 3.
So that being said, I understand that f(x)^2 - 3 = 0 implies that f(x) = sqrt(3).
But then how would one generalize this?
Homework Statement
Use the First Isomorphism Theorem to show that Q[x]/(x^3-3) is isomorphic to {a+b*sqrt(3)}
Homework Equations
First Isomorphism Theorem:
If f: G-> H is a homomorphism then G/ker(f) is isomorphic to im(f)
The Attempt at a Solution
I understand that I need to show...
I'm trying to understand the first isomorphism theorem for groups.
Part of the examples given in the book is showing that Q[x]/(x^3-3) is isomorphic to {a+b*sqrt(3)}
As I understand it, by finding a homomorphism from Q[x] to {a+b*sqrt(3)} in which the kernel is x^3-3, the two are...