Central Extensions of n-Ordered Division Rings

Abstract

We study central extensions of division rings with orderings of higher level. We show that orderings extend to certain immediate and inert extensions. Further, it is proven that any n-ordered division ring can be extended to a n-ordered division ring with almost real closed center. In the last section, an old theorem due to Neumann is generalized: every n-ordered division ring can be extended to a n-ordered division ring containingin its center.