Holomorphy rings and higher level orders on skew fields
The author extends Becker's theory of higher level orders and preorders to division rings as far as this theory can go. Her main tool is an extension of valuation theory from fields to division rings. She also finds a sensible generalization of the concept of Prüfer ring to subrings of division rings. Finally, she shows that all her commutative theorems [Math. Z. 198, No. 4, 545--554 (1988; Zbl 0627.10014)] are valid for division rings.
scientific article; zbMATH DE number 4177217