- #1

- 7

- 0

## Main Question or Discussion Point

Hi guys,

I'm trying to show that [tex]\mathbb{F}_5[x]/(x^2+2)[/tex] and [tex]\mathbb{F}_5[x]/(x^2+3)[/tex] are isomorphic as rings.

As I understand it, I have to find the homomorphism [tex]\phi:R\to S[/tex] which is linear and that [tex]\phi(1)=1[/tex].

I'm just struggling to find what I need to send [tex]x[/tex] to in order to get this work.

I'm trying to show that [tex]\mathbb{F}_5[x]/(x^2+2)[/tex] and [tex]\mathbb{F}_5[x]/(x^2+3)[/tex] are isomorphic as rings.

As I understand it, I have to find the homomorphism [tex]\phi:R\to S[/tex] which is linear and that [tex]\phi(1)=1[/tex].

I'm just struggling to find what I need to send [tex]x[/tex] to in order to get this work.