Ramified Sets Of Pseudotrees
Algorithms for generating random posets, random lattices and random lattice terms are given.
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.
In the paper, the notion of relative polarity in ordered sets is introduced and the lattices of -polars are studied. Connections between -polars and prime ideals, especially in distributive sets, are found.