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Coproducts of bounded distributive lattices: infinite distributivity. (English) Zbl 1121.06011

Summary: It is shown that, if two bounded distributive lattices satisfy the join-infinite distributive law (JID), then their coproduct also satisfies this law. F. M. Yaqub [Acta Math. Hung. 48, 7–10 (1986; Zbl 0612.06008)] 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.

MSC:

06D25 Post algebras (lattice-theoretic aspects)
06D05 Structure and representation theory of distributive lattices
06E15 Stone spaces (Boolean spaces) and related structures
06B30 Topological lattices
08B25 Products, amalgamated products, and other kinds of limits and colimits
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

Citations:

Zbl 0612.06008
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