Plane elliptic geometry over rings

Frieder Knüppel and Edzard Salow

Vol. 123 (1986), No. 2, 337–384

DOI: 10.2140/pjm.1986.123.337

Abstract

The classical model of plane elliptic geometry is a sphere of the real affine space. The points of this model are the pairs of antipodal points of the sphere, and the lines are the great circles of the sphere. Right angles retain their ordinary meaning. This model is isomorphic to the real projective plane, where orthogonality on the set of lines is given by a symmetric bilinear form such that no line is orthogonal to itself.

In the present paper we attempt a foundation and a study of plane elliptic geometry over commutative rings.

Mathematical Subject Classification 2000

Primary: 51F05

Secondary: 51C05

Milestones

Received: 14 November 1984

Revised: 25 June 1985

Published: 1 June 1986