Projective Geometry on Partially Ordered Sets
, and .
Transactions of the American Mathematical Society 266 (1): pp. 319-332 (1981)

A set of axioms is presented for a projective geometry as an incidence structure on partially ordered sets of "points" and "lines". The axioms reduce to the axioms of classical projective geometry in the case where the points and lines are unordered. It is shown that the lattice of linear subsets of a projective geometry is modular and that every modular lattice of finite length is isomorphic to the lattice of linear subsets of some finite-dimensional projective geometry. Primary geometries are introduced as the incidence-geometric counterpart of primary lattices. Thus the theory of finite-dimensional projective geometries includes the theory of finite- 3-dimensional projective Hjelmslev-spaces of level $n$ as a special case. Finally, projective geometries are characterized by incidence properties of points and hyperplanes.
  • @sdo
This publication has not been reviewed yet.

rating distribution
average user rating0.0 out of 5.0 based on 0 reviews
    Please log in to take part in the discussion (add own reviews or comments).