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Some Examples of Distributive Ockham Algebras with de Morgan Skeletons

  • T. S. Blyth

Abstract

A (distributive) Ockham algebra is a bounded distributive lattice L on which there is defined a dual endomorphism f. In such an algebra (L, f) the subset S(L) = {xf; xL} is a subalgebra which we call the skeleton of L; it is a de Morgan algebra precisely when f 3 = f. A study of the class K p, q of Ockham algebras in which f q = f 2p+q for p ≥ 1, q ≥ 0 was initiated by Berman in [2]. The Ockham algebras with de Morgan skeletons thus constitute the class K 1, 1.

Keywords

Distributive Lattice Unary Operation Great Element Hasse Diagram Irreducible Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    R. Beazer, On some small subvarieties of distributive Ockham algebras. Glasgow Math. J., 25, 1984, 175–181.MathSciNetzbMATHCrossRefGoogle Scholar
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    J. Berman, Distributive lattices with an additional unary operation. Aequationes Math., 16, 1977, 165–171.MathSciNetzbMATHCrossRefGoogle Scholar
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    T. S. Blyth and J. C. Varlet, Ockham algebras with de Morgan skeletons. Journal of Algebra, 117, 1988, 165–178.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    H. P. Sankappanavar, Distributive lattices with a dual endomorphism. Z. Math. Logik Grundlag. Math., 31, 1985, 385–392.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • T. S. Blyth
    • 1
  1. 1.Mathematical InstituteUniversity of St AndrewsSt. Andrews, FifeScotland

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