In this paper we shall study a notion of relative annihilator-preserving congruence relation and relative annihilator-preserving homomorphism in the class of bounded distributive semilattices. We shall give a topological characterization of this class of semilattice homomorphisms. We shall prove that the semilattice congruences that are associated with filters are exactly the relative annihilator-preserving congruence relations.
CONICET and Departamento de Matemáticas, Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto 399, 7000, Tandil, Argentina
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