Sets of disjoint elements in free products of lattice-ordered groups

Powell, Wayne B.; Tsinakis, Constantine

doi:10.1090/S0002-9939-1988-0931736-6

Sets of disjoint elements in free products of lattice-ordered groups
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by Wayne B. Powell and Constantine Tsinakis PDF

Proc. Amer. Math. Soc. 104 (1988), 1014-1020 Request permission

Abstract:

We show that for every infinite cardinal number $m$ there exist two totally ordered abelian groups whose free product in any nontrivial variety of lattice-ordered groups has a disjoint set of cardinality $m$. This answers problem 10.7 of [13] and extends the results in [12]. We further prove that for the variety of abelian lattice-ordered groups or the variety of all lattice-ordered groups, the free product of two nontrivial members of the variety will always contain an infinite disjoint set.

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