Unsolvable One-dimensional Lifting Problems for Congruence Lattices of Lattices
نویسندگان
چکیده
Let S be a distributive {∨, 0 }-semilattice. In a previous paper, the second author proved the following result: Suppose that S is a lattice. Let K be a lattice, let φ : Conc K → S be a {∨, 0 }-homomorphism. Then φ is, up to isomorphism, of the form Conc f , for a lattice L and a lattice homomorphism f : K → L. In the statement above, Conc K denotes as usual the {∨, 0 }-semilattice of all finitely generated congruences of K. We prove here that this statement characterizes S being a lattice.
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