Continuous Geometry
：Continuous Geometry
( Princeton Landmarks in Mathematics and Physics )
Publication subTitle ：Continuous Geometry
Publication series ：Princeton Landmarks in Mathematics and Physics
Author： von Neumann John;Halperin Israel
Publisher： Princeton University Press
Publication year： 2016
E-ISBN: 9781400883950
P-ISBN(Paperback): 9780691058931
Subject： O18 geometric topology
Keyword： 数学
Language： ENG
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Description
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.