Some Examples of Distributive Ockham Algebras with de Morgan Skeletons

T. S. Blyth
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T. S. Blyth: University of St Andrews, Mathematical Institute

A chapter in Lattices, Semigroups, and Universal Algebra, 1990, pp 21-28 from Springer

Abstract: 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.

Keywords: Distributive Lattice; Unary Operation; Great Element; Hasse Diagram; Irreducible Algebra (search for similar items in EconPapers)
Date: 1990
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DOI: 10.1007/978-1-4899-2608-1_3

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