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. 
@article{AL_2006_45_2_a4,
     author = {M. V. Semenova},
     title = {Lattices {Embeddable} in {Subsemigroup} {Lattices.} {I.} {Semilattices}},
     journal = {Algebra i logika},
     pages = {215--230},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2006_45_2_a4/}
}
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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/