Abstract
Abstract We prove TheoremA. The cardinal product of two copies of the integers is an amalgamation base for the class of all lattice-ordered groups but their lexicographic product is not. This answers Problem 27 of [Black Swamp Problem Book (W. Charles Holland, ed.), Bowling Green State University, 1982]. We also prove TheoremB. he cardinal product of n copies of the integers is not an amalgamation base for the class of all lattice-ordered groups if n ≥ 3.
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