We use dominions to show that many varieties of lattices have nonsurjective epimorphisms. The variety D of distributive lattices is treated in detail. We show that the dominion in D of a sublattice M ⊆ L is the closure of M under relative complementation in L. This dominion is also the largest sublattice of L in which M is epimorphically embedded. In any variety of lattices larger than D, the dominion of M in L is just M .
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