# Some Examples of Distributive Ockham Algebras with de Morgan Skeletons

Chapter

## 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
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## References

- [1]R. Beazer,
*On some small subvarieties of distributive Ockham algebras*. Glasgow Math. J.,**25**, 1984, 175–181.MathSciNetzbMATHCrossRefGoogle Scholar - [2]J. Berman,
*Distributive lattices with an additional unary operation*. Aequationes Math.,**16**, 1977, 165–171.MathSciNetzbMATHCrossRefGoogle Scholar - [3]T. S. Blyth and J. C. Varlet,
*Ockham algebras with de Morgan skeletons*. Journal of Algebra,**117**, 1988, 165–178.MathSciNetzbMATHCrossRefGoogle Scholar - [4]H. P. Sankappanavar,
*Distributive lattices with a dual endomorphism*. Z. Math. Logik Grundlag. Math.,**31**, 1985, 385–392.MathSciNetzbMATHCrossRefGoogle Scholar

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© Springer Science+Business Media New York 1990