Spectral spaces of semistar operations

Carmelo Antonio Finocchiaro, Dario Spirito, Marco Fontana

Research output: Contribution to journalArticlepeer-review


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
Original languageEnglish
Pages (from-to)2897-2913
JournalJournal of Pure and Applied Algebra
Issue number8
Publication statusPublished - 2016
Externally publishedYes


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