Is it possible to find all commutative $\mathbb{Q}$-algebras which are not integral domains?
An example for such algebra is $\frac{\mathbb{Q}[t]}{(t^2-1)}$. More generally, $\frac{\mathbb{Q}[t]}{(h)}$, where $h \in Q[t]$ is reducible in $\mathbb{Q}[t]$.
Any hints and comments are welcome!