Faulkner geometry
Axioms are presented for a Barbilian geometry of dimension \(n \geq 2\) over a ring for which \(ab = 1\) implies \(ba = 1\). It is shown that any Faulkner geometry (i.e. a Barbilian geometry with additional axioms) of dimension \(n \geq 3\) is coordinatized by a unique associative two-sided units ring \(R\) and that the group generated by all transvections is a group of Steinberg type over \(R\).
scientific article; zbMATH DE number 843599