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Some varieties of semidistributive lattices

Part of the Lecture Notes in Mathematics book series (LNM,volume 1149)

Keywords

  • Lattice Variety
  • Homomorphic Image
  • Universal Algebra
  • Irreducible Element
  • Finite Lattice

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References

  1. Berman, J. and Wolk, B., Free lattices in some small varieties, Algebra Universalis, 10(1980), 269–289.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Birkhoff, G., On the lattice theory of ideals, Bull. Amer. Math. Soc., 40(1934), 613–619.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Birkhoff, G., Lattice Theory, 3rd ed. (1967), Providence, R.I., American Mathematical Society.

    MATH  Google Scholar 

  4. Day, A., A simple solution to the word problem for lattices, Canadian Math. Bull., 13(1970), 253–254.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Day, A., Splitting lattices generate all lattices, Algebra Universalis, 7(1977), 163–169.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Day, A., Characterizations of lattices that are bounded-homomorphic images or sublattices of free lattices, Canadian J. Math., 31(1979), 69–78.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Day, A. and Nation, J.B., A note on finite sublattice of free lattices, Algebra Universalis, 15(1982), 90–94.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Dedekind, R., Über die von drei Moduln erzeugte Dualgruppe, Math. Ann., 53(1900), 371–403.

    CrossRef  MathSciNet  Google Scholar 

  9. Freese, R., Ideal lattices of lattices, Pacific J. Math., 57(1975), 125–133.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Freese, R., The structure of modular lattices of width four with applications to varieties of lattices, Memoirs Amer. Math. Soc., no. 181 (1977), Providence, R.I., American Mathematical Society.

    MATH  Google Scholar 

  11. Freese, R. and Nation, J. B., Covers in free lattices, to appear in Trans. Amer. Math. Soc.

    Google Scholar 

  12. Grätzer, G., Equational classes of lattices, Duke Math. J., 33(1966), 613–622.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Hong, D. X., Covering relations among lattice varieties, Pacific J. Math., 40(1972), 575–603.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Jónsson, B., Algebras whose congruence lattices are distributive, Math. Scand., 21(1967), 110–121.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Jónsson, B., Equational classes of lattices, Math. Scand., 22(1968), 187–196.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Jónsson, B., Varieties of lattices: some open problems, Coll. Math. Soc. János Bolyai, 29(1982), Contributions to Universal Algebra (Esztergom), North Holland, 421–436.

    Google Scholar 

  17. Jónsson, B. and Nation, J. B., A report on sublattices of a free lattice, Coll. Math. Soc. János Bolyai, 17(1977), Contributions to Universal Algebra (Szeged), North Holland, 233–257.

    Google Scholar 

  18. Jónsson and Rival, I., Lattice varieties covering the smallest nonmodular variety, Pacific J. Math., 82(1979), 463–478.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Lee. J. G., Almost distributive lattice varieties, Ph.D. Dissertation, Vanderbilt University, 1983.

    Google Scholar 

  20. McKenzie, R., Equational bases and nonmodular lattice varieties, Trans. Amer. Math. Soc., 174(1972), 1–43.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. Nation, J. B., Bounded finite lattices, Coll. Math. Soc. János Bolyai, 29(1982), Contributions to Universal Algebra (Esztergom), North Holland, 531–533.

    Google Scholar 

  22. Nation, J. B., Finite sublattices of a free lattice, Trans. Amer. Math. Soc., 269(1982), 311–337.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. Rose, H., Nonmodular lattice varieties, Memoris Amer. Math. Soc., no. 292 (1984), Providence, R.I., American Mathematical Society.

    MATH  Google Scholar 

  24. Waterman, A. G., The free lattice with 3 generators over N5, Portugal. Math. 26(1967), 285–288.

    MathSciNet  MATH  Google Scholar 

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© 1985 Springer-Verlag

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Nation, J.B. (1985). Some varieties of semidistributive lattices. In: Comer, S.D. (eds) Universal Algebra and Lattice Theory. Lecture Notes in Mathematics, vol 1149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098466

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  • DOI: https://doi.org/10.1007/BFb0098466

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15691-8

  • Online ISBN: 978-3-540-39638-3

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