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Proceedings of the American Mathematical Society

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

 

 

On free abelian $ l$-groups


Author: Paul Hill
Journal: Proc. Amer. Math. Soc. 38 (1973), 53-58
MSC: Primary 06A60
DOI: https://doi.org/10.1090/S0002-9939-1973-0313159-5
MathSciNet review: 0313159
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Abstract: Let $ F$ denote the free abelian lattice ordered group over an unordered torsion free group $ G$. Necessary and sufficient conditions are given on $ G$ in order for $ F$ to be an $ l$-subgroup of a cardinal product of integers. The result encompasses Weinberg's theorem that the freeness of $ G$ is sufficient. The corresponding embedding theorem for $ F$ is also established whenever $ G$ is completely decomposable and homogeneous.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0313159-5
Keywords: Lattice ordered group, free group, free abelian $ l$-group, cardinal product, subdirect product of integers, homogeneous groups
Article copyright: © Copyright 1973 American Mathematical Society