Ockham algebra

In mathematics, an Ockham algebra is a bounded distributive lattice ${\displaystyle L}$ with a dual endomorphism, that is, an operation ${\displaystyle \sim :L\to L}$ satisfying

• ${\displaystyle \sim (x\wedge y)=\sim x\vee \sim y}$,
• ${\displaystyle \sim (x\vee y)=\sim x\wedge \sim y}$,
• ${\displaystyle \sim 0=1}$,
• ${\displaystyle \sim 1=0}$.

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

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

• 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. 

0.00 (0 votes) Original source: https://en.wikipedia.org/wiki/Ockham algebra. Read more