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Congruence lattices of planar lattices

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References

  1. V. A. Baranskiî, On the independence of the automorphism group and the congruence lattice for lattices, in Abstract of Lectures of the 15th Allsoviet Algebraic Conference (Krasnojarsk, July 1979), 1979, p. 11.

  2. V. A. Baranskiî, On the independence of the automorphism group and the congruence lattice for lattices, Izu. vuzov Matematika, 12 (1984), 12–17.

    Google Scholar 

  3. R. Frucht, Herstellung von Graphen mit vorgegebener abstrakter Gruppe, Compos. Math., 6 (1938), 239–250.

    Google Scholar 

  4. R. Frucht, Lattices with a given group of automorphisms, Canad. J. Math., 2 (1950), 417–419.

    Google Scholar 

  5. N. Funayama and T. Nakayama, On the distributivity of a lattice of lattice-congruences, Proc. Imp. Acad. Tokyo, 18 (1942), 553–554.

    Google Scholar 

  6. G. Grätzer, General Lattice Theory, Academic Press (New York, N. Y.); Birkhäuser Verlag (Basel); Akademie Verlag (Berlin), 1978.

    Google Scholar 

  7. G. Grätzer, Universal Algebra, Second Edition. Springer Verlag (New York, Heidelberg, Berlin, 1979).

    Google Scholar 

  8. G. Grätzer, On the automorphism group and the complete congruence lattice of a complete lattice, Abstract of papers presented to the Amer. Math. Soc. 88T-06-215.

  9. G. Grätzer, Results on the congruence lattice of a lattice, in The Dilworth Theorems. Selected papers of Robert P. Dilworth, Edited by K. P. Bogart, R. Freese, and J. Kung, Birkhäuser Verlag (Basel, Boston, 1989).

    Google Scholar 

  10. G. Grätzer and H. Lakser, Homomorphisms of distributive lattices as restrictions of congruences, Canad. J. Math. 38 (1986), 1122–1134.

    Google Scholar 

  11. G. Grätzer and H. Lakser, On the m-complete congruence lattice and the automorphism group of an m-complete lattice, Abstracts of papers presented to the Amer. Math. Soc. 88T-08-253.

  12. G. Grätzer and H. Lakser, On complete congruence lattices of complete lattices, Trans. Amer. Math. Soc., 327 (1991), 385–405.

    Google Scholar 

  13. G. Grätzer and H. Lakser, On congruence lattices of m-complete lattices, J. Austral. Math. Soc. (Series A), 52 (1992), 57–87.

    Google Scholar 

  14. G. Grätzer and H. Lakser, Homomorphisms of distributive lattices as restrictions of congruences. II. Restrictions of automorphisms, Abstracts of papers presented to the Amer. Math. Soc. 89T-08.

  15. G. Grätzer and E. T. Schmidt, On congruence lattices of lattices, Acta Math. Acad. Sci. Hung., 13 (1962), 179–185.

    Google Scholar 

  16. G. Sabidussi, Graphs with given infinite groups, Monatsh. Math., 64 (1960), 64–67.

    Google Scholar 

  17. E. T. Schmidt, On the length of the congruence lattice of a lattice, Algebra Universalis, 5 (1975), 98–100.

    Google Scholar 

  18. E. T. Schmidt, Homomorphisms of distributive lattices as restrictions of congruences, Acta Sci. math. (Szeged), 51 (1987), 209–215.

    Google Scholar 

  19. S.-K. Teo, Representing finite lattices as complete congruence lattices of complete lattices, Ann. Univ. Sci. Budapest. Eötvös, Sect. Math., 33 (1990), 177–182.

    Google Scholar 

  20. S.-K. Teo, On the length of the congruence lattice of a lattice, Manuscript. University of Manitoba (1988), 1–9.

  21. A. Urquhart, A topological representation theory for lattices, Algebra Universalis, 8 (1978), 45–58.

    Google Scholar 

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This research was supported by the NSERC of Canada.

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Grätzer, G., Lakser, H. Congruence lattices of planar lattices. Acta Math Hung 60, 251–268 (1992). https://doi.org/10.1007/BF00051643

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