The Projective Geometry Over Partially Ordered Skew Fields

Derivative lattices associated with partially ordered linear spaces over skew fields are considered. Properties of the convex projective geometry $$ \mathcal{L} for a space FV field F investigated. The convexity subspaces means Abelian (ab-convexity), which is based on definition subgroup group. It shown that ab-convex directed plays theory same role as subgroups groups. We obtain element-wise description smallest subspace contains given positive element, field. proved if an interpolation F, then, in lattice , union operation completely distributive respect to intersection. pseudo lattice-ordered