Chapter XVII. Properties of Continuous Rings

Chapters in this book

1. Frontmatter i
2. Foreword v
3. Table of Contents x
4. Part I
5. Chapter I. Foundations and Elementary Properties 1
6. Chapter II. Independence 8
7. Chapter III. Perspectivity and Projectivity. Fundamental Properties 16
8. Chapter IV. Perspectivity by Decomposition 24
9. Chapter V. Distributivity. Equivalence of Perspectivity and Projectivity 32
10. Chapter VI. Properties of the Equivalence Classes 42
11. Chapter VII. Dimensionality 54
12. Part II
13. Chapter I. Theory of Ideals and Coordinates in Projective Geometry 63
14. Chapter II. Theory of Regular Rings 69
15. Chapter III. Order of a Lattice and of a Regular Ring 93
16. Chapter IV. Isomorphism Theorems 103
17. Chapter V. Projective Isomorphisms in a Complemented Modular Lattice 117
18. Chapter VI. Definition of L-Numbers; Multiplication 130
19. Chapter VII. Addition of L-Numbers 136
20. Chapter VIII. The Distributive Laws, Subtraction; and Proof that the L-Numbers form a Ring 151
21. Chapter IX. Relations Between the Lattice and its Auxiliary Ring 160
22. Chapter X. Further Properties of the Auxiliary Ring of the Lattice 168
23. Chapter XI. Special Considerations. Statement of the Induction to be Proved 177
24. Chapter XII. Treatment of Case I 191
25. Chapter XIII. Preliminary Lemmas for the Treatment of Case II 197
26. Chapter XIV. Completion of Treatment of Case II. The Fundamental Theorem 199
27. Chapter XV. Perspectivities and Projectivities 209
28. Chapter XVI. Inner Automorphism 217
29. Chapter XVII. Properties of Continuous Rings 222
30. Chapter XVIII. Rank-Rings and Characterization of Continuous Rings 231
31. Part III
32. Chapter I. Center of a Continuous Geometry 240
33. Chapter II. Transitivity of Perspectivity and Properties of Equivalence Classes 264
34. Chapter III. Minimal Elements 277
35. List of Changes from the 1935—37 Edition and comments on the text 283
36. Index 297