Abstract
In this paper we shall discuss some aspects of the relation between the structure of a finite semidistributive lattice L and the set P(L) of its join-prime elements. These investigations were motivated in part by the results of the first author in [2] and [3], wherein finite sublattices of a free lattice which are generated by both their join-prime and meet-prime elements are described. It is well-known that the set of join-prime elements of a finite distributive lattice (which coincides with the set of join-irreducible elements) completely determines the lattice. On the other hand, a finite nondistributive lattice (e.g., M3) may well "have P(L) empty. In a nontrivial finite semidistributive lattice, though, P(L) is never empty (see w and in the presence of Whitman's condition or L being a bounded homomorphic image of a free lattice, we can establish at least some explicit connection between P(L) and the structure of L (w and w For finite lattices in general, we make the following simple observation.
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