Continuous Geometry

von Neumann, John

ISBN 10: 0691058938 / ISBN 13: 9780691058931

Editore: Princeton University Press, Princeton, New Jersey, 1988

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22.5 x 15 cm. xi 299pp. Index. With a foreword by Israel Halperin. Reproduced from notes of lectures on Continuous Geometry given by John von Neumann at Princeton from 1935-37. Part of the Princeton Landmarks in Mathematics series. Codice articolo 79288

Dati bibliografici

Titolo: Continuous Geometry

Casa editrice: Princeton University Press, Princeton, New Jersey

Data di pubblicazione: 1988

Legatura: Paperback

Condizione: Fine

Descrizione articolo

Riassunto:

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.

Recensione:

"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