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Algebra Logika, 2006, Volume 45, Number 2, Pages 215–230 (Mi al143)  

This article is cited in 7 scientific papers (total in 7 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

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

Bibliographic databases:

UDC: 512.56
Received: 05.10.2005
Revised: 02.02.2006

Citation: M. V. Semenova, “Lattices Embeddable in Subsemigroup Lattices. I. Semilattices”, Algebra Logika, 45:2 (2006), 215–230; Algebra and Logic, 45:2 (2006), 124–133

Citation in format AMSBIB
\Bibitem{Sem06}
\by M.~V.~Semenova
\paper Lattices Embeddable in Subsemigroup Lattices. I. Semilattices
\jour Algebra Logika
\yr 2006
\vol 45
\issue 2
\pages 215--230
\mathnet{http://mi.mathnet.ru/al143}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2260332}
\zmath{https://zbmath.org/?q=an:1117.20044}
\transl
\jour Algebra and Logic
\yr 2006
\vol 45
\issue 2
\pages 124--133
\crossref{https://doi.org/10.1007/s10469-006-0011-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33646479141}


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    This publication is cited in the following articles:
    1. M. V. Semenova, “Lattices Embeddable in Subsemigroup Lattices. II. Cancellative Semigroups”, Algebra and Logic, 45:4 (2006), 248–253  mathnet  crossref  mathscinet  zmath
    2. M. V. Semenova, “On lattices embeddable into subsemigroup lattices. III: Nilpotent semigroups”, Siberian Math. J., 48:1 (2007), 156–164  mathnet  crossref  mathscinet  zmath  isi
    3. M. V. Semenova, “On lattices embeddable into subsemigroup lattices. V. Trees”, Siberian Math. J., 48:4 (2007), 718–732  mathnet  crossref  mathscinet  zmath  isi
    4. Semenova M.V., “On lattices embeddable into subsemigroup lattices. IV. Free semigroups”, Semigroup Forum, 74:2 (2007), 191–205  crossref  mathscinet  zmath  isi  elib  scopus
    5. M. V. Semenova, “Embedding Lattices into Derived Lattices”, Proc. Steklov Inst. Math., 278, suppl. 1 (2012), S116–S130  mathnet  crossref  crossref  isi  elib
    6. M. V. Semenova, A. Zamojska-Dzienio, “Lattices of subclasses”, Siberian Math. J., 53:5 (2012), 889–905  mathnet  crossref  mathscinet  isi  elib  elib
    7. M. V. Shvidefski, “Ob odnom klasse reshetok podpolugrupp”, Sib. matem. zhurn., 61:5 (2020), 1177–1193  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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