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Up: TOME 49 (97), no. 1
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Abstract:
We study several properties of lattice and Boolean functions of one argument: being a translation, an endomorphism, a closure operator, and properties related to the composition of functions. The latter properties include inversability, commutativity and the existence of classes of lattice/Boolean functions that are commutative subgroups. It turns out that these semigroups are also lattices. We obtain as a by-product a characterization of distributive lattices.
Key Words: Distributive lattice, Boolean function, lattice function, endomorphism, translation, commutativity of composition.
2000 Mathematics Subject Classification: Primary: 06E30,
Secondary: 06B99.
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