When the Zariski space is a Noetherian space

Abstract

We characterize when the Zariski space $\mathrm{Zar}(K|D)$ (where $D$ is an integral domain, $K$ is a field containing $D$ and $D$ is integrally closed in $K$) and the set $\mathrm{Za}{\mathrm{r}}_{\min }(L|D)$ of its minimal elements are Noetherian spaces.

v2: small correction to Proposition 3.1

Cited by in corpus (2)

• Realization of spaces of commutative rings
• Isolated points of the Zariski space