3 problems

Let $D$ be an integral domain, let $K$ be its quotient field, and let $\mathcal{S}$ be a family of semistar operations on $D$ induced by overrings of $D$. For a quasi-compact famil…

Let $A$ be an integral domain, and let $Y$ be a family of overrings of $A$. Write $\wedge_Y$ for the semistar operation determined by $Y$, and give the relevant space of overrings…

Semistar-counting conjecture. The domain $D$ is a principal ideal domain (PID) if and only if