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De Morgan algebra
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De Morgan algebras
This page is about distributive lattices equipped with a contravariant involution. For Heyting algebras satisfying de Morgan's law, which are also sometimes called “De Morgan algebras”, see De Morgan Heyting algebra.
De Morgan algebras
Definition
A De Morgan algebra is a distributive lattice equipped with a contravariant involution, i.e. a map such that . This implies that satisfies De Morgan’s laws: and .
Examples
- Any Boolean algebra is a De Morgan algebra, with the logical negation.
- Any star-autonomous poset that happens to be a distributive lattice is a De Morgan algebra, with the star-autonomous involution .
- The unit interval is a De Morgan algebra, with .
- The four-point algebra with two parallel lines: with , , and is a small example of a DeMorgan algebra which is not Boolean.
Last revised on October 9, 2022 at 23:42:44.
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