I want to show that $$\mathbb{Z}_3[\sqrt{-5}] /\langle 3, 2 + \sqrt{-5} \rangle \cong \mathbb{Z}_3$$ What bijective map should I build to show the isomorphism relation?
Important Edit : I made a mistake. I meant $\langle 3, 2 + \sqrt{-5} \rangle$ not $\langle 2 + \sqrt{-5} \rangle$
Dividing out by $(2+\sqrt{-5})$ means we "set" $2+\sqrt{-5}=0$, or in other words $\sqrt{-5}=1$. What do you think the isomorphism will be?