50 years of Finite Geometry, the “geometries over finite rings”

Abstract

Whereas for a substantial part, “Finite Geometry" during the past 50 years has focussed on geometries over finite fields, geometries over finite rings that are not division rings have got less attention. Nevertheless, several important classes of finite rings give rise to interesting geometries.

In this paper we bring together some results, scattered over the literature, concerning finite rings and plane projective geometry over such rings. The paper does not contain new material, but by collecting information in one place, we hope to stimulate further research in this area for at least another 50 years of Finite Geometry.