Flat Ideals and Stability in Integral Domains

We introduce the concept of $\mathit{\text{quasi-stable}}$ ideal in an integral domain $D$ (a nonzero fractional ideal $I$ of $D$ is quasi-stable if it is flat in its endomorphism ring $(I\text{\hspace{0.17em}⁣}:I)$) and study properties of domains in which each nonzero fractional ideal is quasi-stable. We investigate some questions about flatness that were raised by S. Glaz and W.V. Vasconcelos in their 1977 paper \cite{GV}.