Abstract
The aim of this paper is to give a direct, simple proof of the well-known theorems — that the Hall ternary ring (R, T) of a Pappian projective plane is a linear ternary ring over a field, and that of a Desarguesian plane is a linear one over a skew field — by making repeated application of the perspectivity theorem in a Pappian plane and the characterization of Desarguesian planes in terms of perspectivities.
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Jagannathan, T.V.S. The ternary rings of Desarguesian and Pappian planes — A simple proof using perspectivities. Geom Dedicata 18, 191–195 (1985). https://doi.org/10.1007/BF00151398
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DOI: https://doi.org/10.1007/BF00151398