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25 Remote Warehouse Mathematics- Geometry and Trigonometry

Other titles in the Princeton Landmarks in Mathematics and Physics series:

Continuous Geometry (Princeton Landmarks in Mathematics and Physics)

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Continuous Geometry (Princeton Landmarks in Mathematics and Physics) Cover

 

Synopses & Reviews

Publisher Comments:

In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Neumann founded the field of continuous geometry.

This book, based on von Neumann's lecture notes, begins with the development of the axioms of continuous geometry, dimension theory, and--for the irreducible case--the function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries, for which irreducibility is not assumed. For students and researchers interested in ring theory or projective geometries, this book is required reading.

Synopsis:

In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Newmann founded the field of continuous geometry. For students and researchers interested in ring theory or projective geometries, von Neumann discusses his findings and their applications.

Table of Contents

Foreword
Foundations and Elementary Properties1
Independence8
Perspectivity and Projectivity. Fundamental Properties16
Perspectivity by Decomposition24
Distributivity. Equivalence of Perspectivity and Projectivity32
Properties of the Equivalence Classes42
Dimensionality54
Theory of Ideals and Coordinates in Projective Geometry63
Theory of Regular Rings69
Appendix 182
Appendix 284
Appendix 390
Order of a Lattice and of a Regular Ring93
Isomorphism Theorems103
Projective Isomorphisms in a Complemented Modular Lattice117
Definition of L-Numbers; Multiplication130
Appendix133
Addition of L-Numbers136
Appendix148
The Distributive Laws, Subtraction; and Proof that the L-Numbers form a Ring151
Appendix158
Relations Between the Lattice and its Auxiliary Ring160
Further Properties of the Auxiliary Ring of the Lattice168
Special Considerations. Statement of the Induction to be Proved177
Treatment of Case I191
Preliminary Lemmas for the Treatment of Case II197
Completion of Treatment of Case II. The Fundamental Theorem199
Perspectivities and Projectivities209
Inner Automorphisms217
Properties of Continuous Rings222
Rank-Rings and Characterization of Continuous Rings231
Center of a Continuous Geometry240
Appendix 1245
Appendix 2259
Transitivity of Perspectivity and Properties of Equivalence Classes264
Minimal Elements277
List of Changes from the 1935-37 Edition and comments on the text by Israel Halperin283
Index297

Product Details

ISBN:
9780691058931
Foreword:
Halperin, Israel
Author:
Halperin, Israel
Foreword by:
Halperin, Israel
Foreword:
Halperin, Israel
Author:
John von Neumann
Author:
Halperin, Israel
Author:
Von Neumann, John
Author:
von, John
Publisher:
Princeton University Press
Location:
Princeton, N.J.
Subject:
Geometry - General
Subject:
Geometry
Subject:
Advanced
Subject:
Topology
Subject:
Geometry, projective
Subject:
Continuous groups.
Subject:
Continuous geometries.
Subject:
Mathematics
Subject:
Mathematics-Geometry and Trigonometry
Copyright:
Edition Description:
Trade paper
Series:
Princeton landmarks in mathematics and physics
Series Volume:
no. 37
Publication Date:
April 1998
Binding:
TRADE PAPER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Yes
Pages:
312
Dimensions:
9 x 6 in 16 oz

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Related Subjects

Religion » Comparative Religion » General
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
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Continuous Geometry (Princeton Landmarks in Mathematics and Physics) New Trade Paper
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Product details 312 pages Princeton University Press - English 9780691058931 Reviews:
"Synopsis" by , In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Newmann founded the field of continuous geometry. For students and researchers interested in ring theory or projective geometries, von Neumann discusses his findings and their applications.
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