Zur Fortsetzung von o-Stellen angeordneter Divisionsalgebren. (On extensions of o-places of ordered division algebras) (Q1112333)

It is well-known that any place of a commutative field F can be extended to a place of any commutative extension field of F. An analogous result for ternary fields is not true in general. The present authors study this question for an ordered (not necessarily associative) division algebra K which contains an ordered division subalgebra F. They show that any order compatible place of F can be extended to an order compatible place of K. Geometrically, this means that any order preserving epimorphism of an ordered projective plane \({\mathcal F}\) of Lenz class at least V can be extended to an order preserving epimorphism of any ordered projective plane of Lenz class at least V which contains \({\mathcal F}\) as a subplane. Recently a similar result for nearfields has been proved by \textit{F. Kalhoff} [Result Math. 15, 66-74 (1989)].