Spectral spaces of semistar operations

Carmelo Antonio Finocchiaro, Dario Spirito, Marco Fontana

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung


We investigate, from a topological point of view, the classes of spectral semistar operations and of eab semistar operations, following methods recently introduced in [11], [13]. We show that, in both cases, the subspaces of finite type operations are spectral spaces in the sense of Hochster and, moreover, that there is a distinguished class of overrings strictly connected to each of the two types of collections of semistar operations. We also prove that the space of stable semistar operations is homeomorphic to the space of Gabriel–Popescu localizing systems, endowed with a Zariski-like topology, extending to the topological level a result established in [14]. As a side effect, we obtain that the space of localizing systems of finite type is also a spectral space. Finally, we show that the Zariski topology on the set of semistar operations is the same as the b-topology defined recently by B. Olberding
Seiten (von - bis)2897-2913
FachzeitschriftJournal of Pure and Applied Algebra
PublikationsstatusVeröffentlicht - 2016
Extern publiziertJa


Untersuchen Sie die Forschungsthemen von „Spectral spaces of semistar operations“. Zusammen bilden sie einen einzigartigen Fingerprint.

Dieses zitieren