The Connected Components of the Projective Line over a Ring

Abstract

The main result of the present paper is that the projective line over a ring $R$ is connected with respect to the relation "distant" if, and only if, $R$ is a $G{E}_2$-ring.

References in corpus (2)

• Projective Representations I. Projective lines over rings
• Extending the Concept of Chain Geometry

Cited by in corpus (11)

• On bijections that preserve complementarity of subspaces
• On distant-isomorphisms of projective lines
• The Dual of a Chain Geometry
• Jordan homomorphisms and harmonic mappings
• From pentacyclic coordinates to chain geometries, and back
• The Shortest Path Problem for the Distant Graph of the Projective Line Over the Ring of Integers
• Von Staudt's theorem revisited
• Projective completions of Jordan pairs. Part I: The generalized projective geometry of a Lie algebra
• Projective Ring Lines and Their Generalisations
• The Cayley Graph of Neumann Subgroups
• Projective completions of Jordan pairs Part II. Manifold structures and symmetric spaces