TITLE: What is the quotient ring $\Bbb Z[x]/(2x-3)$?
QUESTION [8 upvotes]: Is there a good description for the quotient ring $\Bbb Z[x]/(2x-3)$?

That is, does the quotient ring $\Bbb Z[x]/(2x-3)$ isomorphic to some other ring with a simple description?
I know that $\Bbb Z[x]/(2x-3)$ is an integral domain since $2x-3$ is irreducible in $\Bbb Z[x]$, so the quotient ring is indeed well defined. But I don't know if we can go further than that.

REPLY [5 votes]: $R=\Bbb Z[x]/(2x-3)\cong\Bbb Z[1/2]$ via the map which sends $x-1\mapsto 1/2$.
Then this is a subset of $\Bbb Q$, so $\text{frac}(R)\subseteq\Bbb Q$. However since $\Bbb Z\subseteq R$ we have that $\text{frac}(\Bbb Z)\subseteq\text{frac}(R)$, hence we have that $\text{frac}(R)=\Bbb Q$.