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The graphs of join-semilattices and the shape of congruence lattices of particle lattices

Pavel Růžička (2017)

Commentationes Mathematicae Universitatis Carolinae

We attach to each 0 , -semilattice S a graph G S whose vertices are join-irreducible elements of S and whose edges correspond to the reflexive dependency relation. We study properties of the graph G S both when S is a join-semilattice and when it is a lattice. We call a 0 , -semilattice S particle provided that the set of its join-irreducible elements satisfies DCC and join-generates S . We prove that the congruence lattice of a particle lattice is anti-isomorphic to the lattice of all hereditary subsets of...

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