Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings (Lecture Notes in Mathematics)
Edition: 1 edition
Publisher: Springer
Published: November 23, 1999
Language: eng
Format: Paperback
Number of pages: 300
ISBN-13: 9783540664604
Subjects: Algebra; Algebraic number theory; Geometry; Topology; Semialgebraic sets; Mathematics; Algebraic Geometry; Rings; Science/Mathematics; Rings (Algebra); Ordered algebraic structures; Algebra - General; General; Geometry - Algebraic; Mathematics / Algebra / General; Mathematics / Geometry / Algebraic; Mathematics-Geometry - Algebraic; Medical-General; formally real field; Group Theory
Description: 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.