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Continuous geometry

Author: John Von Neumann; Israel Halperin
Publisher: Princeton, N.J. : Princeton University Press, ©1998.
Series: Princeton landmarks in mathematics and physics.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
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Based on von Neumann's lecture notes, this book begins with the development of the axioms of continuous geometry, dimension theory, and - for the irreducible case - the function D(a). The properties  Read more...

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Document Type: Book
All Authors / Contributors: John Von Neumann; Israel Halperin
ISBN: 0691058938 9780691058931
OCLC Number: 40296837
Notes: Includes index.
Description: xi, 299 p. : ill. ; 23 cm.
Contents: Foreword Independence Perspectivity and Projectivity. Fundamental Properties Perspectivity by Decomposition Distributivity. Equivalence of Perspectivity and Projectivity Properties of the Equivalence Classes Dimensionality Theory of Ideals and Coordinates in Projective Geometry Theory of Regular Rings Appendix 1 Appendix 2 Appendix 3 Order of a Lattice and of a Regular Ring Isomorphism Theorems Projective Isomorphisms in a Complemented Modular Lattice Definition of L-Numbers; Multiplication Appendix Addition of L-Numbers Appendix The Distributive Laws, Subtraction; and Proof that the L-Numbers form a Ring Appendix Relations Between the Lattice and its Auxiliary Ring Further Properties of the Auxiliary Ring of the Lattice Special Considerations. Statement of the Induction to be Proved Treatment of Case I Preliminary Lemmas for the Treatment of Case II Completion of Treatment of Case II. The Fundamental Theorem Perspectivities and Projectivities Inner Automorphisms Properties of Continuous Rings Rank-Rings and Characterization of Continuous Rings Center of a Continuous Geometry Appendix 1 Appendix 2 Transitivity of Perspectivity and Properties of Equivalence Classes Minimal Elements List of Changes from the 1935-37 Edition and comments on the text by Israel Halperin Index
Series Title: Princeton landmarks in mathematics and physics.
Responsibility: John von Neumann ; foreword by Israel Halperin.

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"This historic book should be in the hands of everyone interested in rings and projective geometry."--R. J. Smith, The Australian Journal of Science "Much in this book is still of great value, partly Read more...

 
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