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Postulates For Distributive Lattices

  • Marlow Sholander
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Many sets of postulates have been given for distributive lattices and for Boolean algebra. For a description of some of the most interesting and for references to others the reader is referred to Birkhoff's “Lattice Theory”[1]. In this paper we give sets of postulates which have some intrinsic interest because of their simplicity. In the first two sections binary operations are used to describe a distributive lattice by 2 identities in 3 variables and a Boolean algebra by 3 identities in 3 variables. In the third section a ternary operation is used to describe distributive lattices with 0 and J by 2 identities in 5 variables.

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References
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[1] Birkhoff, Garrett, Lattice Theory, Amer. Math. Soc. Colloquium Publications, vol. XXV' 1948.
[2] Croisot, R., Axiomatique des lattices distributives, Can. J. Math., vol. 3, (1951), pp. 2427.
[3] Grau, A. A., Ternary operations and Boolean algebra, Ph.D. Thesis, University of Michigan, 1944.
[4] Kiss, S. A. and Birkhoff, Garrett, A ternary operation in distributive lattices, Bull. Amer. Math. Soc, vol. 53 (1947), 749752.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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