Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings

• Main Authors: Schwartz, Niels (Author, http://id.loc.gov/vocabulary/relators/aut), Madden, James J. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.
• Edition: 1st ed. 1999.
• Series: Lecture Notes in Mathematics, 1712
• Subjects: Algebra.; Number theory.; Geometry.; Algebraic geometry.; Nonassociative rings.; Rings (Algebra).; Number Theory.; Algebraic Geometry.; Non-associative Rings and Algebras.
• Physical Description: XIII, 279 p. online resource.
• ISBN: 9783540482840
• ISSN: 0075-8434 ;
• DOI: 10.1007/BFb0093968

The book lays algebraic foundations for real geometry through a systematic investigation of partially ordered rings of semi-algebraic functions. Real spectra serve as primary geometric objects, the maps between them are determined by rings of functions associated with the spectra. The many different possible choices for these rings of functions are studied via reflections of partially ordered rings. Readers should feel comfortable using basic algebraic and categorical concepts. As motivational background some familiarity with real geometry will be helpful. The book aims at researchers and graduate students with an interest in real algebra and geometry, ordered algebraic structures, topology and rings of continuous functions.