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