Recent content by JackTheLad

Yeah, unfortunately I do have to show the explicit isomorphism (we're supposed to do it 'the long way')

Actually, I think x --> 2x might do it, because x^2 + 2 \equiv 0 (2x)^2 + 2 \equiv 0 4x^2 + 2 \equiv 0 4(x^2 + 3) \equiv 0 x^2 + 3 \equiv 0 Is that all that's required?

Actually, I think x --> 2x might do it, because x^2 + 2 \equiv 0 (2x)^2 + 2 \equiv 0 4x^2 + 2 \equiv 0 4(x^2 + 3) \equiv 0 x^2 + 3 \equiv 0 Is that all that's required?

Homework Statement Hi guys, I'm trying to show that \mathbb{F}_5[x]/(x^2+2) and \mathbb{F}_5[x]/(x^2+3) are isomorphic as rings. The Attempt at a Solution As I understand it, I have to find the homomorphism \phi:R\to S which is linear and that \phi(1)=1. I'm just struggling to find...

Hi guys, I'm trying to show that \mathbb{F}_5[x]/(x^2+2) and \mathbb{F}_5[x]/(x^2+3) are isomorphic as rings. As I understand it, I have to find the homomorphism \phi:R\to S which is linear and that \phi(1)=1. I'm just struggling to find what I need to send x to in order to get this work.

For posterity, two functions which fit nicely are f(x) = x g(x) = x-1 (I had tried lots of functions but they worked; not very helpful response)

Homework Statement Find two functions f, g \in C[0,1] (i.e. continuous functions on [0,1]) which do not satisfy 2 ||f||^2_{sup} + 2 ||g||^2_{sup} = ||f+g||^2_{sup} + ||f-g||^2_{sup} (where || \cdot ||_{sup} is the supremum or infinity norm) Homework Equations Parallelogram identity...