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; x ∈ L} 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.
NATO Grant 85/0532 is gratefully acknowledged.
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References
R. Beazer, On some small subvarieties of distributive Ockham algebras. Glasgow Math. J., 25, 1984, 175–181.
J. Berman, Distributive lattices with an additional unary operation. Aequationes Math., 16, 1977, 165–171.
T. S. Blyth and J. C. Varlet, Ockham algebras with de Morgan skeletons. Journal of Algebra, 117, 1988, 165–178.
H. P. Sankappanavar, Distributive lattices with a dual endomorphism. Z. Math. Logik Grundlag. Math., 31, 1985, 385–392.
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© 1990 Springer Science+Business Media New York
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Blyth, T.S. (1990). Some Examples of Distributive Ockham Algebras with de Morgan Skeletons. In: Almeida, J., Bordalo, G., Dwinger, P. (eds) Lattices, Semigroups, and Universal Algebra. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2608-1_3
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DOI: https://doi.org/10.1007/978-1-4899-2608-1_3
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