Amalgamating abelian ordered groups

Abstract

Sums, or amalgamations, of two abelian ordered groups with a subgroup amalgamated are constructed in two ways. These constructions are used to investigate the structure of the class of all amalgamations with the given groups and subgroup fixed, where the class is partially ordered in a natural way. In particular, necessary and sufficient conditions are found for there to be (a) exactly one amalgamation, up to equivalence, and (b) exactly one minimal amalgamation, up to equivalence.