On the rank of incidence matrices in projective Hjelmslev spaces

Imbrex geometries

We introduce an axiom on strong parapolar spaces of diameter 2, which arises naturally in the framework of Hjelmslev geometries. This way, we characterize the Hjelmslev-Moufang plane and its relatives (line Grassmannians, certain half-spin geometries and Segre geometries). At the same time we provide a more general framework for a lemma of Cohen, which is widely used to study parapolar spaces. ...

Spreads in Projective Hjelmslev Spaces over Finite Chain Rings

We prove a necessary and sufficient condition for the existence of spreads in the projective Hjelmslev geometries PHG Rn 1 R . Further, we give a construction of projective Hjelmslev planes from spreads that generalizes the familiar construction of projective planes from spreads in PG n q .

Optimal Arcs in Hjelmslev Spaces of Large Dimension

In this paper, we present various results on arcs in projective threedimensional Hjelmslev spaces over finite chain rings of nilpotency index 2. A table is given containing exact values and bounds for projective arcs in the geometries over the two chain rings with four elements.

On Incidence Matrices of Finite Projective and Affine Spaces

It is welt-known that the rank of each incidence matrix of all points vs. all e-spaces of a finite d-dimensional projective or affine space is the number of points of the geometry, where 1 <_e<-d-1 (see [1], p. 20). In this note we shall generalize this fact: Theorem. Let 0 <-e < f <= d-e-1, and let Me, l be an incidence matrix of all e-spaces vs. all f-spaces of PG(d, q) or AG(d, q). Then the ...

The dual construction for arcs in projective Hjelmslev spaces