Vol. 65, No. 1, 1976

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Amalgamated sums of abelian l-groups

Keith Pierce

Vol. 65 (1976), No. 1, 167–173

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.

Mathematical Subject Classification 2000
Primary: 06A60, 06A60
Secondary: 20K99, 08A25
Received: 5 March 1975
Published: 1 July 1976
Keith Pierce