Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 136 / 1 / b / ii

The element $T$ belongs to the fraction field of $R=\mathbb{C}[T^2,T^3]$ and is integral over $R$, since it satisfies the monic polynomial $X^2-T^2$. But $T\notin R$. Thus $R$ is not integrally closed domain and hence is not a Dedekind domain.