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Article Dans Une Revue Forum Mathematicum Année : 2002

Unsolvable one-dimensional lifting problems for congruence lattices of lattices

Jiri Tuma
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Résumé

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 $\varphi$: Con K $\to$ S be a {?, 0}-homomorphism. Then $\varphi$ is, up to isomorphism, of the form Conc f, for a lattice L and a lattice homomorphism f : K $\to$ L. In the statement above, Conc K denotes as usual the {?, 0}-semilattice of all ?nitely generated congruences of K. We prove here that this statement characterizes S being a lattice.
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Dates et versions

hal-00004023 , version 1 (21-01-2005)

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Jiri Tuma, Friedrich Wehrung. Unsolvable one-dimensional lifting problems for congruence lattices of lattices. Forum Mathematicum, 2002, 14 (4), pp.483--493. ⟨10.1515/form.2002.022⟩. ⟨hal-00004023⟩
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