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.

Continuous Geometry

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Paperback / softback by John von Neumann , Israel Halperin

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In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled... Read more

    Publisher: Princeton University Press
    Publication Date: 10/05/1998
    ISBN13: 9780691058931, 978-0691058931
    ISBN10: 0691058938

    Number of Pages: 312

    Non Fiction , Mathematics & Science , Education

    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.

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