Recent content by CurtBuck

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?

Yeah, it was supposed to be Q[x]/(x^2-3)

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...