Embedding Ordered Valued Domains into Division Rings

We study some classes of ordered domains that are embeddable in division rings. We prove the ordered version of the Cohn–Lichtman embedding theorem for valued domains. A question of Glass is answered in the negative. Furthermore, we prove that universal enveloping algebras of Lie algebras over formally real fields can be embedded into ordered division rings. The author acknowledges the financial support from the state budget by the Slovenian Research Agency (project no. Z1-9570-0101-06).