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 [37,38].
Spectral spaces of semistar operations
Finocchiaro C. A.;
2016-01-01
Abstract
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 [37,38].File | Dimensione | Formato | |
---|---|---|---|
spectral-spaces-semistar-operations.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
PUBBLICO - Pubblico con Copyright
Dimensione
308.52 kB
Formato
Adobe PDF
|
308.52 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.