ISBN: 3-540-66460-2
TITLE: Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings
AUTHOR: Schwartz, Niels; Madden, James J.
TOC:

Introduction 1
1 Preordered and partially ordered rings 21
2 Reflective subcategories 35
3 Totally ordered and real closed fields 43
4 Real spectra of preordered rings 45
5 Epimorphisms of reduced porings 51
6 Punctions and representable porings 55
7 Semialgebraic functions 63
8 Comparing reflectors 79
9 Constructing reflectors 93
10 Hclosed epireflectors 107
11 Quotientclosed reflectors 125
12 The real closure reflector 133
13 Arities of reflectors and approximations by Hclosed reflectors 161
14 Epimorphic extensions of reduced porings 167
15 Essential monoreflectors 183
16 Reflections of totally ordered fields 189
17 von Neumann regular frings 201
18 Totally ordered domains 209
19 Reduced frings 217
20 Rings of continuous piecewise polynomial functions 229
21 Rings of continuous piecewise rational functions 233
22 Discontinuous semialgebraic functions 241
23 The lattice of Hclosed monoreflectors 253
Bibliography 259
List of categories 266
Index 275
END
