CHAPTER 19

Geometry over Rings

Ferdinand D. VELDKAMP

Department of Mathematics, Utrecht University,
Budapestlaan 6, 3508 TA Utrecht, The Netherlands

Contents

Introduction

1. Free modules and their subspaces

2. Rings of stable rank 2

3. Algebraic description of

4. Axiomatic approach: V-spaces

5. Collineations and affine collineations. Coordinatization of V-spaces

6. Homomorphisms of V-spaces

7. Projective spaces over full matrix rings

8. Klingenberg spaces

9. Hjelmslev geometries

10. Transvection V-planes

11. Faulkner planes

12. Affine ring planes and Barbilian domains

13. Leiß ner planes

14. Open problems

References