Geodesic
Lattices Embeddable in Subsemigroup Lattices. I. Semilattices
Algebra i logika, Tome 45 (2006) no. 2, pp. 215-230.

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V. B. Repnitskii showed that any lattice embeds in some subsemilattice lattice. In his proof, use was made of a result by D. Bredikhin and B. Schein, stating that any lattice embeds in the suborder lattice of a suitable partial order. We present a direct proof of Repnitskii's result, which is independent of Bredikhin–Schein's, giving the answer to a question posed by L. N. Shevrin and A. J. Ovsyannikov. We also show that a finite lattice is lower bounded iff it is isomorphic to the lattice of subsemilattices of a finite semilattice that are closed under a distributive quasiorder.
Keywords: lattice, subsemilattice lattice, lower bounded lattice, partial order. 
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M. V. Semenova. Lattices Embeddable in Subsemigroup Lattices. I. Semilattices. Algebra i logika, Tome 45 (2006) no. 2, pp. 215-230. http://geodesic.mathdoc.fr/item/AL_2006_45_2_a4/

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