On the algebraic representation of projectively embeddable affine geometries (Q1904266)

The author in his earlier work has introduced a concept of affine geometry which includes the congruence class geometry of modules. In this article it is shown how to each projective lattice geometry with a fixed hyperplane there is associated an affine geometry; isomorphic copies of the latter are called projectively embeddable affine geometries. The main result of the paper is the following theorem: For an affine geometry \(A\) of dimension at least 2 the following are equivalent: (a) \(A\) is projectively embeddable into an Arguesian projective geometry. (b) \(A\) is module induced.