Functions on Distributive Lattices with the Congruence Substitution Property: Some Problems of Grätzer from 1964
نویسنده
چکیده
Let L be a bounded distributive lattice. For k 1, let Sk (L) be the lattice of k-ary functions on L with the congruence substitution property (Boolean functions); let S(L) be the lattice of all Boolean functions. The lattices that can arise as Sk (L) or S(L) for some bounded distributive lattice L are characterized in terms of their Priestley spaces of prime ideals. For bounded distributive lattices L and M, it is shown that S1 (L)$S1 (M) implies Sk (L)$Sk (M). If L and M are finite, then Sk (L)$Sk (M) implies L$M. Some problems of Gra tzer dating to 1964 are thus solved. 2000 Academic Press
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