Continuous Geometry

(Paperback)

Publishing Details

Classifications

Physical Properties

Description

In his work on rings of operators in Hilbert space, the author discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, John 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.

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

Author Bio

John von Neumann (1903-1957) was a Permanent Member of the Institute for Advanced Study in Princeton.