A construction for topological non-desarguesian affine Hjelmslev planes (Q1085795)

As a generalization of the result of Skornjakov and Salzmann that a locally compact connected ternary field produces a topological affine plane, the authors prove that a topological biternary ring generates a topological affine Hjelmslev plane. Examples are given of topological biternary rings of topological dimensions 2, 4, 8 and 16 which generate non-desarguesian affine Hjelmslev translation planes of dimension 4, 8, 16 and 32.