Jordan homomorphisms and harmonic mappings

Abstract

We show that each Jordan homomorphism $R\to R^{\prime }$ of rings gives rise to a harmonic mapping of one connected component of the projective line over $R$ into the projective line over $R^{\prime }$. If there is more than one connected component then this mapping can be extended in various ways to a harmonic mapping which is defined on the entire projective line over $R$.

References in corpus (4)

• Projective Representations I. Projective lines over rings
• The Connected Components of the Projective Line over a Ring
• Extending the Concept of Chain Geometry
• The Dual of a Chain Geometry

Cited by in corpus (3)

• On distant-isomorphisms of projective lines
• Von Staudt's theorem revisited
• Projective Ring Lines and Their Generalisations