Let $I=(4t+3)$ be an ideal in $\mathbb{Z}[t]$. Find a subring of $\mathbb{R}$ isomorphic to $\mathbb{Z}[t]/I$.
If $(4t+3)$ were monic, this question would be easily answered but since it isn't I'm having problems seeing exactly how $\mathbb{Z}[t]/I$ could be isomorphic to a subring of the reals.
Consider $7t+a\in\mathbb{Z}[t]$. The remainder is $3t+(a-3)$.By looking at the remainder of polynomials divided by $4t+3$, it's fairly clear that elements in $\mathbb{Z}[t]/I$ have the form $a+bt$ for $a\in\mathbb{Z}$ and $b\in\mathbb{Z}/4\mathbb{Z} \Rightarrow \mathbb{Z}[t]/I\cong \mathbb{Z}\times \mathbb{Z}/4\mathbb{Z}$. But how can this be isomorphic to a subring of $\mathbb{R}$?