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Lattices isomorphic to subsemilattice lattices of finite trees

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Algebra and Logic Aims and scope

We give a syntactic description of the class of lattices isomorphic to subsemilattice lattices of finite trees as well as of the class of lattices isomorphic to subsemilattice lattices of finite n-ary trees for any positive n.

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References

  1. L. N. Shevrin and A. Ja. Ovsyannikov, Semigroups and Their Subsemigroup Lattices, Kluwer, Dordrecht (1996).

    MATH  Google Scholar 

  2. K. V. Adaricheva, “The structure of finite lattices of subsemilattices,” Algebra Logika, 30, No. 4, 385-404 (1991).

    MathSciNet  Google Scholar 

  3. V. A. Gorbunov and V. I. Tumanov, “A class of lattices of quasivarieties,” Algebra Logika, 19, No. 1, 59-80 (1980).

    Article  MathSciNet  Google Scholar 

  4. M. V. Semenova, “On lattices embeddable into subsemigroup lattices. V. Trees,” Sib. Mat. Zh., 48, No. 4, 894-913 (2007).

    MATH  MathSciNet  Google Scholar 

  5. L. N. Shevrin, “Basic problems in the theory of projectivities of semilattices,” Math. Sb., 66(108), No. 4, 568-597 (1965).

    Google Scholar 

  6. F. Wehrung, “Sublattices of complete lattices with continuity conditions,” Alg. Univ., 53, Nos. 2/3, 149-173 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  7. R. N. McKenzie, “Equational bases and non-modular lattice varieties,” Trans. Am. Math. Soc., 174, No. 1, 1-43 (1972).

    Article  MathSciNet  Google Scholar 

  8. R. Freese, J. Ježek, and J. B. Nation, Free Lattices, Math. Surv. Monogr., 42, Am. Math. Soc., Providence, RI (1995).

  9. A. P. Huhn, “Schwach distributive Verbände. I,” Acta Sci. Math. (Szeged), 33, 297-305 (1972).

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    M. V. Semenova

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    K. M. Skorobogatov

Authors
  1. M. V. Semenova
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  2. K. M. Skorobogatov
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Correspondence to M. V. Semenova.

Additional information

Supported by the CRDF (grant No. KYM1-2852-BI-07), by the German Scientific Research Society (DFG) and RFBR (grant No. 06-01-04002), by the Council for Grants (under RF President) for State Support of Young Candidates of Science (project MK-3988.2007.1), by the Council for Grants (under RF President) for State Support of Leading Scientific Schools (grants NSh-4413.2006.1 and NSh-344.2008.1), and by SB RAS (Young Researchers Support grant No. 11).

Translated from Algebra i Logika, Vol. 48, No. 4, pp. 471-494, July-August, 2009.

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Semenova, M.V., Skorobogatov, K.M. Lattices isomorphic to subsemilattice lattices of finite trees. Algebra Logic 48, 268–281 (2009). https://doi.org/10.1007/s10469-009-9058-9

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  • DOI: https://doi.org/10.1007/s10469-009-9058-9

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