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Proceedings of the American Mathematical Society

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

 

 

Free products of abelian $ l$-groups are cardinally indecomposable


Authors: Wayne B. Powell and Constantine Tsinakis
Journal: Proc. Amer. Math. Soc. 86 (1982), 385-390
MSC: Primary 06F20; Secondary 08B25
DOI: https://doi.org/10.1090/S0002-9939-1982-0671199-6
MathSciNet review: 671199
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Abstract: We show that a well-known theorem of Baer and Levi concerning the impossibility of simultaneous decomposition of a group into a free product and a direct sum has an analogue for abelian lattice ordered groups. Specifically we prove that an abelian lattice ordered group cannot be decomposed both into a free product and into a cardinal sum.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0671199-6
Article copyright: © Copyright 1982 American Mathematical Society