Some Examples of Distributive Ockham Algebras with de Morgan Skeletons

  • T. S. Blyth


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.


Distributive Lattice Unary Operation Great Element Hasse Diagram Irreducible Algebra 
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  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
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    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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