  We prove that, under mild assumptions, for all positive integers $\ell$, the
zero set of the discriminant ideal $D_{\ell}(R/Z(R); tr)$ of a prime polynomial
identity (PI) algebra $R$ coincides with the zero set of the modified
discriminant ideal $MD_{\ell}(R/Z(R); tr)$ of $R$. Furthermore, we prove that,
when $\ell$ is the square of the PI-degree of $R$, this zero set is precisely
the complement of the Azumaya locus of $R$. This description is used to
classify the Azumaya loci of the mutiparameter quantized Weyl algebras at roots
of unity. As another application, we prove that the zero set of the top
discriminant ideal of a prime PI algebra $R$ coincides with the singular locus
of the center of $R$, provided that the discriminant ideal has height at least
2, $R$ has finite global dimension and $R$ is a Cohen-Macaulay module over its
center.
