This article is cited in 8 papers

Lattices Embeddable in Subsemigroup Lattices. I. Semilattices

M. V. Semenova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: 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.

UDC: 512.56

Received: 05.10.2005
Revised: 02.02.2006

 English version: Algebra and Logic, 2006, 45:2, 124–133

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