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.
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