Theorem

Krull's valuation domain theorem

If $G$ is a totally ordered Abelian group, then there exists a valuation domain with divisibility group $G$.

Reference(s)

  • W. Brandal. Constructing Bézout domains. (1976) @ Theorem 1.1 p 385
  • W. Krull. Allgemeine Bewertungstheorie. (1932) @ p 164