Let $I$ be an ideal in a Noetherian  quasi-unmixed local ring $(R,\mathfrak m).$ 

Let $q(I)=\overline{I}\cap I^{sat}$ where $I^{sat}=\cup_{n\geq 0}I:\mathfrak m^n.$ Then $q(I)$ is called *relative integral closure* of $I.$

**Question** Is there any example of a principal ideal $I$ (i.e. $I=(a)$) such that $I\neq q(I).$ 

I know that in normal domains, $I=q(I)$ for all principal ideal $I.$