Coproducts of bounded distributive lattices: infinite distributivity |
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Authors: | Jonathan David Farley |
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Institution: | (1) Department of Applied Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States of America |
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Abstract: | 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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Keywords: | coproduct (generalized) Post algebra Priestley duality (bounded) distributive lattice (partially) ordered topological space |
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