Spectral spaces of semistar operations

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• 作者：Carmelo A. Finocchiaro ^{carmelo@mat.uniroma3.it" class="auth_mail" title="E-mail the corresponding author} ; Marco Fontana ; ^{fontana@mat.uniroma3.it" class="auth_mail" title="E-mail the corresponding author} ; Dario Spirito ^{spirito@mat.uniroma3.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：13A15 ; 13G05 ; 13B10 ; 13E99 ; 13C11 ; 14A05
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：220
• 期：8
• 页码：2897-2913
• 全文大小：499 K

文摘

We investigate, from a topological point of view, the classes of spectral semistar operations and of eab semistar operations, following methods recently introduced in  and . 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  and .