Summary
It is shown that, if two bounded distributive lattices satisfy the join-infinite distributive law (JID), then their coproduct also satisfies this law. In 1986, Yaqub proved that generalized Post algebras with a finite lattice of constants satisfy JID, and stated that, in general, it is not known whether a generalized Post algebra satisfies JID when its lattice of constants satisfies JID. In this note, the statement is proved.
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Farley, J. Coproducts of bounded distributive lattices: infinite distributivity. Acta Math Hung 112, 269–273 (2006). https://doi.org/10.1007/s10474-006-0079-8
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DOI: https://doi.org/10.1007/s10474-006-0079-8