An Embedding Theorem for Commutative Lattice-Ordered Domains

Abstract

In a recent paper Conrad and Dauns have shown that a finitely-rooted lattice-ordered field $R$, in which multiplication by a positive special element is a lattice homomorphism, can be embedded in a formal power series $l$-field with real coefficients, provided that the value group of $R$ is torsion-free. In this note it is shown that their theorem is true when $R$ is a commutative integral domain.