# Projective Hjelmslev plane

From Groupprops

This term is related to: incidence geometry

View other terms related to incidence geometry | View facts related to incidence geometry

Template:Incidence structure property

This is a variation of projective plane|Find other variations of projective plane |

## Contents

## Definition

### Symbol-free definition

A **projective Hjelmslev plane** is an incidence structure satisfying the following properties:

- Given any two points, there is at least one line incident with both of them, and given any two lines, there is at least one point incident with both of them
- There exists a canonical surjective homomorphism onto a projective plane such that two points (resp. lines) are in the same fibre if and only if the number of lines (resp. points) incident to both is more than 1.

## Relation with other properties

### Stronger properties

### Related properties

## References

*Finite Geometries* by Peter Dembowski, *Appendix 7.2*