Gabriel filters in real closed rings |
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| Authors: | N Schwartz |
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| Institution: | Fakult?t für Mathematik und Informatik, Universit?t Passau, Postfach 2540, D-94030 Passau, Germany, DE
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| Abstract: | Real closed rings arise in semi-algebraic geometry and topology as well as in the investigation of partially ordered rings.
It is shown that localizations of real closed rings with respect to Gabriel filters, or more generally: multiplicative filters,
are again real closed. Thus, real closedness is preserved under a large number of important ring theoretic constructions.
For a few particularly simple cases the multiplicative filters are classified and the localizations are determined.
Received: August 26, 1996 |
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| Keywords: | ,f-ring, real closed ring, valuation ring, Gabriel filter, Gabriel localization, ring of quotiens, prime ideal, scheme,,,,,,ring of sections, real spectrum, |
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