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The Dual of a Chain Geometry

Andrea Blunck, Hans Havlicek

Abstract

We introduce and discuss the dual of a chain geometry. Each chain geometry is canonically isomorphic to its dual. This allows us to show that there are isomorphisms of chain geometries that arise from antiisomorphisms of the underlying rings.

The Dual of a Chain Geometry

Abstract

We introduce and discuss the dual of a chain geometry. Each chain geometry is canonically isomorphic to its dual. This allows us to show that there are isomorphisms of chain geometries that arise from antiisomorphisms of the underlying rings.

Paper Structure

This paper contains 5 sections, 3 theorems, 20 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The Dual of a Chain Geometry
  4. Compatibility and Dual Compatibility
  5. Isomorphisms

Key Result

Theorem 3.1

Let $\Sigma(K,R)$ be a chain geometry. Then the mapping is an isomorphism of $\Sigma(K,R)$ onto its dual.

Theorems & Definitions (11)

  • Theorem 3.1
  • Remark 3.2
  • Remark 3.3
  • Theorem 4.1
  • Remark 4.2
  • Example 4.3
  • Remark 5.1
  • Theorem 5.2
  • Remark 5.3
  • Remark 5.4
  • ...and 1 more