Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 39, No. 2, pp. 461-466 (1998)

Pappus' Theorem for Ring-geometries

Thorsten Pfeiffer

Zelterstrasse 6, D-55545 Bad Kreuznach, Germany

Abstract: A famous result, due to Hilbert, states for a projective plane over a division ring $K$ the equivalence of Pappus' theorem and the commutativity of $K$.
In this paper we extend this result to the projective plane over an arbitrary ring.

Keywords: ring-geometry, Pappus' theorem

Classification (MSC91): 06A15, 06C, 51A05, 51A10

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