Unsolvable one-dimensional lifting problems for congruence lattices of lattices
Copyright policy )Unsolvable one-dimensional lifting problems for congruence lattices of lattices
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 $��$: Con K $\to$ S be a {���, 0}-homomorphism. Then $��$ 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.
Lattice ideals, congruence relations, compact congruences, congruence, Lattice, Semilattices, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], distributive semilattice, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], General Mathematics (math.GM), amalgamation, 06B10, 06E05, 06E05, FOS: Mathematics, Mathematics - General Mathematics, 06B10, Congruence Lattice Problem
Lattice ideals, congruence relations, compact congruences, congruence, Lattice, Semilattices, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], distributive semilattice, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], General Mathematics (math.GM), amalgamation, 06B10, 06E05, 06E05, FOS: Mathematics, Mathematics - General Mathematics, 06B10, Congruence Lattice Problem
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