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

MSC:

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

Zbl 0445.03041
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References:

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