Projective planes over rings
The author considers associative rings R with a unit element and defines a generalized projective plane p(R), based on four axioms adapted from \textit{F. D. Veldkamp} [Geom. Dedicata 11, 285-308 (1981; Zbl 0468.51001)] except one that is replaced by a weaker property. A coordinatization theorem is stated but without proof due to its length. This theorem is not quite satisfying since two additional assumptions are required, which are not fulfilled in every projective ring plane p(R). One is valid in such a plane if R is commutative and the stable rank of R is less than or equal to three. An example of a projective ring plane is given where this property does not hold.
scientific article; zbMATH DE number 4028265
scientific article