ABSTRACT
A subring B of a skew field F is called a valuation ring of F if x ∈ F\B implies x-1 ∈ B. We say (F,B) is a valued skew field. The lattice of right ideals as well as the lattice of left ideals of a valuation ring are totally ordered, i.e. such a ring is a chain domain with F as its skew field of quotients.
