Von Neumann, John, Halperin, Israel 　著

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目次

Foreword Independence Perspectivity and Projectivity. FundamentalProperties Perspectivity by Decomposition Distributivity. Equivalence ofPerspectivity and Projectivity Properties of the Equivalence ClassesDimensionality Theory of Ideals and Coordinates in Projective Geometry Theoryof Regular Rings Appendix 1 Appendix 2 Appendix 3 Order of a Lattice and of aRegular Ring Isomorphism Theorems Projective Isomorphisms in a ComplementedModular Lattice Definition of L-Numbers; Multiplication Appendix Addition ofL-Numbers Appendix The Distributive Laws, Subtraction; and Proof that theL-Numbers form a Ring Appendix Relations Between the Lattice and itsAuxiliary Ring Further Properties of the Auxiliary Ring of the LatticeSpecial Considerations. Statement of the Induction to be Proved Treatment ofCase I Preliminary Lemmas for the Treatment of Case II Completion ofTreatment of Case II. The Fundamental Theorem Perspectivities andProjectivities Inner Automorphisms Properties of Continuous Rings Rank-Ringsand Characterization of Continuous Rings Center of a Continuous GeometryAppendix 1 Appendix 2 Transitivity of Perspectivity and Properties ofEquivalence Classes Minimal Elements List of Changes from the 1935-37 Editionand comments on the text by Israel Halperin Index