Vol. 104, No. 2, 1983

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Free products in the class of abelian l-groups

Wayne Bruce Powell and Constantine Tsinakis

Vol. 104 (1983), No. 2, 429–442

The main objective of this paper is to present several constructions of free products in the class of abelian l-groups which are sufficiently concrete to allow for an in depth examination of their structure. Some applications of these constructions are discussed, and it is shown that abelian l-group free products satisfy the subalgebra property. Further, some questions on free l-groups over group free products are considered for a variety of l-groups which is either abelian or contains the representable l-groups. Finally, a general observation is made about countable chains and countable disjoint sets in free algebras.

Mathematical Subject Classification 2000
Primary: 06F20
Secondary: 06F25
Received: 1 January 1981
Published: 1 February 1983
Wayne Bruce Powell
Constantine Tsinakis