# Homework Help: Isomorphic rings

1. Mar 21, 2010

### JackTheLad

1. The problem statement, all variables and given/known data
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.

3. 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 what I need to send $$x$$ to in order to get this work.

2. Mar 21, 2010

### JackTheLad

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?

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