E-Book, Englisch, Band 22, 312 Seiten
von Neumann Continuous Geometry
1. Auflage 2016
ISBN: 978-1-4008-8395-0
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
E-Book, Englisch, Band 22, 312 Seiten
Reihe: Princeton Landmarks in Mathematics and Physics
ISBN: 978-1-4008-8395-0
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
No detailed description available for "Continuous Geometry".
Weitere Infos & Material
Foreword
Foundations and Elementary Properties 1
Independence 8
Perspectivity and Projectivity. Fundamental Properties 16
Perspectivity by Decomposition 24
Distributivity. Equivalence of Perspectivity and Projectivity 32
Properties of the Equivalence Classes 42
Dimensionality 54
Theory of Ideals and Coordinates in Projective Geometry 63
Theory of Regular Rings 69
Appendix 1 82
Appendix 2 84
Appendix 3 90
Order of a Lattice and of a Regular Ring 93
Isomorphism Theorems 103
Projective Isomorphisms in a Complemented Modular Lattice 117
Definition of L-Numbers; Multiplication 130
Appendix 133
Addition of L-Numbers 136
Appendix 148
The Distributive Laws, Subtraction; and Proof that the L-Numbers form a Ring 151
Appendix 158
Relations Between the Lattice and its Auxiliary Ring 160
Further Properties of the Auxiliary Ring of the Lattice 168
Special Considerations. Statement of the Induction to be Proved 177
Treatment of Case I 191
Preliminary Lemmas for the Treatment of Case II 197
Completion of Treatment of Case II. The Fundamental Theorem 199
Perspectivities and Projectivities 209
Inner Automorphisms 217
Properties of Continuous Rings 222
Rank-Rings and Characterization of Continuous Rings 231
Center of a Continuous Geometry 240
Appendix 1 245
Appendix 2 259
Transitivity of Perspectivity and Properties of Equivalence Classes 264
Minimal Elements 277
List of Changes from the 1935-37 Edition and comments on the text by Israel Halperin 283
Index 297
