1. INTEGRAL DOMAINS WHOSE SIMPLE OVERRINGS ARE INTERSECTIONS OF LOCALIZATIONS.
- Author
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Fontana, Marco, Houston, Evan, and Lucas, Thomas
- Subjects
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RING theory , *INTERSECTION theory , *PRUFER rings , *INTEGRAL domains , *LOCALIZATION theory , *ALGEBRAIC geometry , *CATEGORIES (Mathematics) - Abstract
Call a domain R an sQQR-domain if each simple overring of R, i.e., each ring of the form R[u] with u in the quotient field of R, is an intersection of localizations of R. We characterize Prüfer domains as integrally closed sQQR-domains. In the presence of certain finiteness conditions, we show that the sQQR-property is very strong; for instance, a Mori sQQR-domain must be a Dedekind domain. We also show how to construct sQQR-domains which have (non-simple) overrings which are not intersections of localizations. [ABSTRACT FROM AUTHOR]
- Published
- 2005
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