Gabriel filters in real closed rings | Zendy

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Gabriel filters in real closed rings

Author(s) -

Niels Schwartz

Publication year - 1997

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050027

Subject(s) - mathematics , multiplicative function , pure mathematics , ring (chemistry) , simple (philosophy) , algebraic number , topology (electrical circuits) , algebra over a field , mathematical analysis , combinatorics , philosophy , chemistry , organic chemistry , epistemology

. 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.

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