Some local-global principles for ordered projective planes

✍ Scribed by Franz Kalhoff

• Publisher: Springer
• Year: 1989
• Tongue: English
• Weight: 971 KB
• Volume: 32
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00181437

✦ Synopsis

Extending the classical theorem of Baer and Krull and related results to arbitrary projective planes we study the compatibility between epimorphisms and halforderings of projective planes. Further, by geometrical means, the classical constructions of finest, ordercompatible valuations and of finest, order-compatible valuations coarser than given valuations are imitated for arbitrary projective planes. This allows us to make a first attack towards trivialization of fans in projective planes.

1. EPIMORPHISMS, PLACES AND HALFORDERINGS

We shall denote the points (lines) of a projective plane H = (~, if, I) by lower case (upper case) letters. Let GH be the intersection of two different lines G and