Hans Havlicek
We establish a version of von Staudt's theorem on mappings which preserve harmonic quadruples for projective lines over (not necessarily commutative) rings with "sufficiently many" units, in particular 2 has to be a unit.
This paper contains 4 sections, 5 theorems, 47 equations.
Theorem 1
Let $M$ and $M'$ be free modules of rank $2$ over rings $R$ and $R'$, respectively. Furthermore, let $R$ satisfy the two conditions: Let $\mu:{\mathbb P}(M)\to {\mathbb P}(M')$ be a harmonicity preserver. Choose any connected component, say $C$, of the distant graph $({\mathbb P}(M),{\mathop{\mathrm{\triangle}}\nolimits})$. Then there exist a basis $(a_{0},a_{1})$ of $M$, a basis $(a_{0}',a_{1}')
