Pacific Journal of Mathematics

A nonassociative extension of the class of distributive lattices.

E. Fried and G. Grätzer

Article information

Source
Pacific J. Math., Volume 49, Number 1 (1973), 59-78.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102945268

Mathematical Reviews number (MathSciNet)
MR0340128

Zentralblatt MATH identifier
0282.06008

Subjects
Primary: 06A20

Citation

Fried, E.; Grätzer, G. A nonassociative extension of the class of distributive lattices. Pacific J. Math. 49 (1973), no. 1, 59--78. https://projecteuclid.org/euclid.pjm/1102945268


Export citation

References

  • [1] B. Banasehewski, Injectivityand essential extensions in equational classes of algebras, Proceedings of the Conference on Universal Algebra, October, 1969, (Queen's University, Kingston, 1970), 131-147.
  • [2] R. Balbes, Protective and injective distributive lattices, Pacific J. Math., 21 (1967), 405-420.
  • [3] A. Day, Injectivityin congruence distributive equational classes, Thesis, McMaster University, 1970.
  • [4] A. Day, A note on the congruence extension property, Algebra Universalis, 1 (1971), 234-235.
  • [5] E. Fried, Tournamentsand nonassociative lattices, Ann. Univ. Sci. Budapest Etvs Sect. Math., 13 (1970), 151-164.
  • [6] E. Fried and G. Gratzer, On some classes of nonassociative lattices, To appear.
  • [7] G. Gratzer, Universal Algebra, The University Series in Higher Mathematics, D. Van Nostrand Co., Princeton, N. J., 1968.
  • [8] G. Gratzer, Lattice Theory, First Concepts and Distributive Lattices, W. H. Freeman and Co., San Francisco, Calif., 1971.
  • [9] G. Gratzer and H. Lakser, Identities for equational classes generated bytournaments, Notices Amer. Math. Soc, 18 (1971), 794.
  • [10] G. Gratzer and E. T. Schmidt, Ideals and congruence relations in lattices, Acta Math. Acad. Sci. Hungar, 9 (1958), 137-175.
  • [11] G. Gratzer and B. Wolk, Finite projective distributive lattices, Canad. Math. Bull., 13 (1970), 139-140.
  • [12] B. Jnsson, Extensionsof relationalstructures,Symposium on the Theory of Models, North-Holland Publ. Co., Amsterdam, 1965, 146-157.
  • [13] B. Jnsson, Algebras whose congruence lattices are distributive,Math. Scand., 21 (1967), 110-121.
  • [14] J. Kagan and R. Quackenbush, Self-dual closure algebras, Manuscript.
  • [15] R. Padmanabhan, Equationaltheory of idempotent algebras, Algebra Universalis, 2 (1972), 57-61.
  • [16] H. L. Skala, Trellis theory, Algebra Universalis, 1 (1971), 218-233.