A class 𝒦 of algebraic
structures is said to have the amalgamation property if, whenever G, H1, and H2 are
in 𝒦 and σ1: G → H1 and σ2: G → H2 are embeddings, then for some L in 𝒦 there
are embeddings τ1;H1→ L and τ2: H2→ L such that σ1τ1= σ2τ2. Since this
property has important universal-algebraic implications, this author has attempted to
determine which well-known classes of abelian lattice-ordered groups (l-groups) have
the amalgamation property. Theorem 1 lists those that do, and Theorem 2
lists those that do not. Finally, we focus our attention on one important
class—Archimedian l-groups—in which the amalgamation property fails, and
derive some sufficient conditions on G, H1, and H2 for amalgamation to
occur.
