Ockham algebra

In mathematics, an Ockham algebra is a bounded distributive lattice L with a dual endomorphism, that is, an operation ∼:L->L satisfying

* ∼(x∧y)=∼x∨∼y,
* ∼(x∨y)=∼x∧∼y,
* ∼0=1,
* ∼1=0.

They were introduced by Berman,[1] and were named after William of Ockham by Urquhart.[2] Ockham algebras form a variety.

## Examples

Examples of Ockham algebras include Boolean algebras, De Morgan algebras, Kleene algebras, and Stone algebras.

## References

1. ↑ Berman, Joel (February 1977). "Distributive lattices with an additional unary operation" (in en). Aequationes Mathematicae 15 (1): 118–118. doi:10.1007/BF01837887. ISSN 0001-9054. http://link.springer.com/10.1007/BF01837887.
2. ↑ Urquhart, Alasdair (1979). "Distributive lattices with a dual homomorphic operation" (in en). Studia Logica 38 (2): 201–209. doi:10.1007/BF00370442. ISSN 0039-3215. http://link.springer.com/10.1007/BF00370442.

## Further reading

* Hazewinkel, Michiel, ed. (2001), "Ockham algebra", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=o/o110030
* Blyth, Thomas Scott; Varlet, J. C. (1994). Ockham algebras. Oxford University Press. ISBN 978-0-19-859938-8.

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