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Continuous Geometry
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John von Neumann
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Preface by:
Israel Halperin
Language:
English
Published/Copyright:
1998
About this book
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.
Author / Editor information
John von Neumann (1903-1957) was a Permanent Member of the Institute for Advanced Study in Princeton.
Reviews
"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
"This historic book should be in the hands of everyone interested in rings and projective geometry."---R. J. Smith, The Australian Journal of Science
Topics
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Part I
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 2, 2016
eBook ISBN:
9781400883950
Pages and Images/Illustrations in book
Main content:
312
eBook ISBN:
9781400883950
Keywords for this book
Theorem; Ideal (ring theory); Axiom; Modular lattice; Dimension function; Geometry; Automorphism; Boolean algebra (structure); Division algebra; Special case; Hilbert space; Orthogonalization; Bounded operator; Principal ideal; Addition; Irreducibility (mathematics); Matrix ring; Existential quantification; Semi-simplicity; Unbounded operator; Baer ring; Lattice (order); Partially ordered set; Infimum and supremum; Big O notation; Module (mathematics); Lipschitz continuity; Homogeneous coordinates; Uniqueness theorem; Transitive relation; Complex number; Dedekind cut; Dimension; Abstract algebra; Join and meet; Integral domain; Linear equation; Characterization (mathematics); Mathematical induction; Polynomial; Hermitian adjoint; Transpose; Identity element; Upper and lower bounds; Dimension (vector space); Set (mathematics); Relative dimension; Subset; Irreducible component; Non-Desarguesian plane; Associative property; Greatest element; Orthogonal complement; Congruence relation; Subsequence; Limit point; Computation; Dimension theory (algebra); Variable (mathematics); Linear combination; Zero element; Direct sum; Arithmetic; Direct proof; Hypercomplex number; Empty set; Dedekind–MacNeille completion; Ring (mathematics); Summation; Linear space (geometry)
Audience(s) for this book
College/higher education;Professional and scholarly;
