关于射影Desar gues平面的除环

Desargues命题和除环有下面关系:公理法定义的射影平面中Desargues命题成立的充分必要条件是该平面是代数地定义在除环上的,本文给出上述结论的必要性的一种证法;藉助合射群的“保心同态”构作除环,进而阐明Desargues射影平面可以代数地定义在该除环上。

On the Division Ring of Desarguesian Projective Plane

The connexion between Desargues' proposition and a division ring is that Desargues' proposition is true in a projective plane (defined synt- hetically) if and only if this projective plane is a projective plane over a division ring (defined algebraically). This paper discusses a method, used to prove the necessity of the above conclusion, which constructs a division ring with "center preserving homomorphism" of elation group and expounds that Desarguesian projective plane can be defined algebra- ically over this division ring.