Vol. 43, No. 3, 1972

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Amalgamating abelian ordered groups

Keith Pierce

Vol. 43 (1972), No. 3, 711–723

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.

Mathematical Subject Classification
Primary: 06A60
Received: 30 August 1971
Revised: 11 September 1972
Published: 1 December 1972
Keith Pierce