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Non-compact subsets of the Zariski space of an integral domain by Spirito, Dario is a scholarly article available to read on EtoBox.

What is Non-compact subsets of the Zariski space of an integral domain about?

Let $V$ be a minimal valuation overring of an integral domain $D$ and let $\mathrm{Zar}(D)$ be the Zariski space of the valuation overrings of $D$. Starting from a result in the theory of semistar operations, we prove a criterion under which the set $\mathrm{Zar}(D)\setminus\{V\}$ is not compact. We then use it to prove that, in many cases, $\mathrm{Zar}(D)$ is not a Noetherian space, and apply it to the study of the spaces of Kronecker function rings and of Noetherian overrings.

Author

Spirito, Dario

Published

2017

Language

EN