A construction of an ordered division ring with a rank one valuation
Let \((k,P_ k)\) be an ordered field and \(\Gamma\) be a dense additive subgroup of \({\mathbb{R}}\). We construct a noncommutative ordered division ring (D,P) and a compatible valuation v on (D,P) such that (i) the value group of v is \(\Gamma\) and (ii) the residue division ring \((\bar D_ v,\bar P_ v)\) is order isomorphic to \((k,P_ k)\). This problem is interesting, because in effect, we are constructing the `simplest' or in some sense the smallest noncommutative ordered division ring.
scientific article; zbMATH DE number 4108952