Spaces of orderings and abstract real spectra / Murray A. Marshall
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1636Langue : anglais.Éditeur : Berlin : Springer, 1996ISBN: 9783540617297.ISSN: 1617-9692.Sujet MSC : 12D15, Field theory and polynomials - Real and complex fields, Fields related with sums of squares11E81, Forms and linear algebraic groups, Algebraic theory of quadratic forms; Witt groups and rings
12J20, Field theory and polynomials - Topological fields, General valuation theory for fields
14P05, Algebraic geometry - Real algebraic and real analytic geometry, Real algebraic sets
13J30, Commutative algebra - Topological rings and modules, Real algebraEn-ligne : Springerlink | Zentralblatt | MathSciNet
This book is a comprehensive and self-contained introduction into the theory of spaces of orderings and abstract real spectra. It starts on a level suitable for a beginner, but the reader is expected to know elementary facts about ordered fields and valuations, and elementary commutative ring theory.
Chapter I makes the reader acquainted with the theory of orderings on fields and the connections to valuation theory.
Chapters II, III and IV introduce the reduced theory of quadratic forms and spaces of orderings, summing up all the important aspects and facts of this theory.
The rest of the book (Chapters V–VIII) is dedicated to the theory of abstract real spectra, starting out with the real spectrum of a ring. The author considers various sets of axioms defining abstract real spectra and proves that they are in fact equivalent, which is highly non-trivial, and are among the main contributions of these notes. (Zentralblatt)
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