Strong De Morgan’s law and the spectrum of a commutative ring. (English) Zbl 0562.18005

The ”strong De Morgan’s law” in a topos is the assertion that the object of truth-values is (internally) linearly ordered. In Lect. Notes Math. 753, 479-491 (1979; Zbl 0445.03041), the reviewer showed that this condition holds in the topos of sheaves on a topological space X iff every closed suspace of X is extremally disconnected. The main result of this paper is that the condition holds for the spectrum of a Noetherian domain R iff R is a Dedekind domain (an example is given to show that the Noetherian condition cannot be dropped).
Reviewer: P.T.Johnstone


18B25 Topoi
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
03G30 Categorical logic, topoi


Zbl 0445.03041
Full Text: DOI


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