Free products of abelian 𝑙-groups are cardinally indecomposable

Powell, Wayne B.; Tsinakis, Constantine

doi:10.1090/S0002-9939-1982-0671199-6

Free products of abelian $l$-groups are cardinally indecomposable
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Proc. Amer. Math. Soc. 86 (1982), 385-390 Request permission

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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The distributive lattice free product as a sublattice of the abelian

-group free product

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