Projective Hjelmslev plane

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This term is related to: incidence geometry
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This is a variation of projective plane|Find other variations of projective plane |

Definition

Symbol-free definition

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

  1. 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
  2. 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