Let $I$ be a non-zero non-trivial ideal of $R:=\mathbb{C}[t]$. It is known that $I=(f)$, for some $f \in R$.
If $I$ is a prime or maximal ideal, then $\frac{R}{I}$ is an integral domain or a field, respectively.
If, for example $I=(t^2)$, then $\frac{R}{I}$ is not an integral domain.
Is there something interesting to say about $\frac{R}{I}$ in general?
By interesting I mean to find all isomorphism classes, for $I$ not prime.
Any comments and hints are welcome!