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- catalog abstract "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.".
- catalog contributor b11476789.
- catalog contributor b11476790.
- catalog created "c1999.".
- catalog date "1999".
- catalog date "c1999.".
- catalog dateCopyrighted "c1999.".
- catalog description "Includes bibliographical references (p. [259]-265) and index.".
- catalog description "Preface -- List of contents -- Introduction -- Preordered and partially ordered rings -- Reflective subcategories -- Totally ordered and real closed fields -- Real spectra of preordered rings: Epimorphisms of reduced porings -- Functions and representable porings -- Semi-algebraic functions -- Comparing reflectors -- Constructing reflectors -- H-closed epireflectors -- Quotient-closed reflectors -- The real closure reflector -- Arities of reflectors and approximations by H-closed reflectors -- Epimorphic extensions of reduced porings -- Essential monoreflectors -- Reflections of totally ordered fields -- von Neumann regular f-rings -- Totally ordered domains -- Reduced f-rings -- Rings of continuous piecewise polynomial functions -- Rings of continuous piecewise rational functions -- Discontinuous semi-algebraic functions -- The lattice of H-closed monoreflectors -- Bibliography -- List of categories -- Index.".
- catalog 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.".
- catalog extent "xii, 279 p. :".
- catalog identifier "3540664602 (softcover : alk. paper)".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1712.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1712".
- catalog issued "1999".
- catalog issued "c1999.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog subject "510 s 512/.4 21".
- catalog subject "Algebra.".
- catalog subject "Geometry, algebraic.".
- catalog subject "Mathematics.".
- catalog subject "Ordered algebraic structures.".
- catalog subject "QA3 .L28 no. 1712 QA564".
- catalog subject "Rings (Algebra)".
- catalog subject "Semialgebraic sets.".
- catalog tableOfContents "Preface -- List of contents -- Introduction -- Preordered and partially ordered rings -- Reflective subcategories -- Totally ordered and real closed fields -- Real spectra of preordered rings: Epimorphisms of reduced porings -- Functions and representable porings -- Semi-algebraic functions -- Comparing reflectors -- Constructing reflectors -- H-closed epireflectors -- Quotient-closed reflectors -- The real closure reflector -- Arities of reflectors and approximations by H-closed reflectors -- Epimorphic extensions of reduced porings -- Essential monoreflectors -- Reflections of totally ordered fields -- von Neumann regular f-rings -- Totally ordered domains -- Reduced f-rings -- Rings of continuous piecewise polynomial functions -- Rings of continuous piecewise rational functions -- Discontinuous semi-algebraic functions -- The lattice of H-closed monoreflectors -- Bibliography -- List of categories -- Index.".
- catalog title "Semi-algebraic function rings and reflectors of partially ordered rings / Niels Schwartz, James J. Madden.".
- catalog type "text".