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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


Authors: Wayne B. Powell and Constantine Tsinakis
Journal: Proc. Amer. Math. Soc. 104 (1988), 1014-1020
MSC: Primary 06F15
DOI: https://doi.org/10.1090/S0002-9939-1988-0931736-6
MathSciNet review: 931736
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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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DOI: https://doi.org/10.1090/S0002-9939-1988-0931736-6
Article copyright: © Copyright 1988 American Mathematical Society