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Bounded distributive lattices with operators. (English) Zbl 0855.06009

Summary: Generalizing a known result about Boolean algebras with operators, we show that every distributive lattice with operators, \({\mathcal A}\), can be embedded in a doubly algebraic distributive lattice with complete operators, \({\mathcal A}^\sigma\), in such a way that every identity that holds in \({\mathcal A}\) also holds in \({\mathcal A}^\sigma\).

MSC:

06D05 Structure and representation theory of distributive lattices
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
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