Continuous Geometry

By: John von Neumann, Israel Halperin (Foreword by)

Write A Review

Paperback | 20 July 1998

At a Glance

Paperback
312 Pages

Dimensions(cm)
25.4 x 19.6 x 254

Paperback

RRP $190.00

$148.75

22%OFF

or 4 interest-free payments of $37.19 with

or

Ships in 3 to 5 business days

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.

Industry Reviews

"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 because it cannot be found elsewhere ... partly because of the very clear and comprehensible presentation. This makes the book valuable for a first study of continuous geometry as well as for research in this field."--F. D. Veldkamp, Nieuw Archief voor Wiskunde

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Geometry

The Maths Book

Big Ideas Simply Explained

Hardcover

RRP $42.99

$32.99

23%
OFF

Grade 4 Geometry and Measurement

Kumon Math Workbooks

Paperback

RRP $16.99

$13.75

19%
OFF

Grade 3 Geometry and Measurement

Paperback

RRP $16.99

$13.75

19%
OFF

Geometry

Grades 6 - 8

Paperback

RRP $24.99

$18.75

25%
OFF

Intro to Geometry

Grades 6 - 8

Paperback

RRP $24.99

$18.99

24%
OFF

Grade 6 Geometry and Measurement

Kumon Math Workbooks

Paperback

RRP $16.99

$13.75

19%
OFF

Essential Trigonometry - Isabella Hughes

$19.75

10%
OFF

Grade 1 Geometry & Measurement

Kumon Math Workbooks

Paperback

RRP $16.99

$13.75

19%
OFF

Calculus

3rd Edition

Hardcover

RRP $97.95

$80.75

18%
OFF

Algebraic Topology

Paperback

RRP $75.95

$64.99

14%
OFF

Crocheting Adventures with Hyperbolic Planes

Tactile Mathematics, Art and Craft for all to Explore, Second Edition

Paperback

RRP $58.99

$53.75

The Golden Ratio

Divine Beauty of Mathematics

Hardcover

RRP $59.99

$42.99

28%
OFF

Metrics, Norms And Integrals

An Introduction To Contemporary Analysis

Paperback

RRP $131.99

$118.99

10%
OFF

Introduction to Lie Algebras : Finite and Infinite Dimension - J. I. Hall

$195.75

Rigid Local Systems and Sporadic Simple Groups - Nicholas Michael Katz

$305.75

Weinstein Handlebodies for Complements of Smoothed Toric Divisors

Paperback

$219.99

Mapping Analytic Surgery to Homology, Higher Rho Numbers and Metrics ofPositive Scalar Curvature

Paperback

$219.99

Foreword
Foundations and Elementary Properties	p. 1
Independence	p. 8
Perspectivity and Projectivity. Fundamental Properties	p. 16
Perspectivity by Decomposition	p. 24
Distributivity. Equivalence of Perspectivity and Projectivity	p. 32
Properties of the Equivalence Classes	p. 42
Dimensionality	p. 54
Theory of Ideals and Coordinates in Projective Geometry	p. 63
Theory of Regular Rings	p. 69
	p. 82
	p. 84
	p. 90
Order of a Lattice and of a Regular Ring	p. 93
Isomorphism Theorems	p. 103
Projective Isomorphisms in a Complemented Modular Lattice	p. 117
Definition of L-Numbers; Multiplication	p. 130
Appendix	p. 133
Addition of L-Numbers	p. 136
Appendix	p. 148
The Distributive Laws, Subtraction; and Proof that the L-Numbers form a Ring	p. 151
Appendix	p. 158
Relations Between the Lattice and its Auxiliary Ring	p. 160
Further Properties of the Auxiliary Ring of the Lattice	p. 168
Special Considerations. Statement of the Induction to be Proved	p. 177
Treatment of Case I	p. 191
Preliminary Lemmas for the Treatment of Case II	p. 197
Completion of Treatment of Case II. The Fundamental Theorem	p. 199
Perspectivities and Projectivities	p. 209
Inner Automorphisms	p. 217
Properties of Continuous Rings	p. 222
Rank-Rings and Characterization of Continuous Rings	p. 231
Center of a Continuous Geometry	p. 240
Appendix 1	p. 245
Appendix 2	p. 259
Transitivity of Perspectivity and Properties of Equivalence Classes	p. 264
Minimal Elements	p. 277
List of Changes from the 1935-37 Edition and comments on the text by Israel Halperin	p. 283
Index	p. 297
Table of Contents provided by Publisher. All Rights Reserved.

Continuous Geometry

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Geometry

The Maths Book

Big Ideas Simply Explained

Grade 4 Geometry and Measurement

Kumon Math Workbooks

Grade 3 Geometry and Measurement

Geometry

Grades 6 - 8

Intro to Geometry

Grades 6 - 8

Grade 6 Geometry and Measurement

Kumon Math Workbooks

Essential Trigonometry

College Geometry

Sacred Geometry

Philosophy and Practice

Grade 1 Geometry & Measurement

Kumon Math Workbooks

Calculus

3rd Edition

Algebraic Topology

Crocheting Adventures with Hyperbolic Planes

Tactile Mathematics, Art and Craft for all to Explore, Second Edition

The Golden Ratio

Divine Beauty of Mathematics

Metrics, Norms And Integrals

An Introduction To Contemporary Analysis

Introduction to Lie Algebras

Finite and Infinite Dimension

The Practice of Algebraic Curves

A Second Course in Algebraic Geometry

Introduction to Lie Algebras

Finite and Infinite Dimension

The Practice of Algebraic Curves

A Second Course in Algebraic Geometry

Rigid Local Systems and Sporadic Simple Groups

RoCK Blocks for Double Covers of Symmetric Groups and Quiver Hecke Superalgebras

Iwasawa Theory and Its Perspective, Volume 3

Weinstein Handlebodies for Complements of Smoothed Toric Divisors

Mapping Analytic Surgery to Homology, Higher Rho Numbers and Metrics ofPositive Scalar Curvature

This product is categorised by