A finite dimensional commutative ring $R$ with unity is called equidimensional if all its minimal prime ideals have same dimension (dimension of a prime ideal $\mathfrak p$ is defined to be Krull dimension of the ring $R/\mathfrak p$) and every maximal ideal has the height same as dimension of the ring.
I want to have an example of a Noetherian domain which is not equidimensional.
Note that $R$ cannot be a finite type $k$ algebra, neither it can be local.
Thank you.