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Show that a quotient of the following rings is a field.

I know that the answer is simple, but I don’t know how to do this proof. I was trying to construct the ring in question but couldn’t find a way to do this. Any help?

You need to show that the following are isomorphisms of rings:

$R/\mathbb{0}\cong \mathbb{F}$
$R/\mathbb{1}\cong R$
$(R/\mathbb{1})+\mathbb{0}\cong R$
$(R/\mathbb{1})\times(R/\mathbb{0})\cong R$

Now $R/\mathbb{1}\cong R$ is easy because $R/\mathbb{1}$ is isomorphic to an ideal of $R$. For (1) you just need to apply the definition of quotient. For (3) and (4) see

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