Order, lattices, ordered algebraic structures Boolean algebras Concept
Residuated lattice
Summary
A residuated lattice is a lattice with a monoid multiplication that has left and right division operations, called residuals. The residuals are characterised by an adjunction with the multiplication and the order. Heyting algebras, Boolean algebras, lattice-ordered groups and the lattices of ideals of a ring are examples. Residuated lattices are the algebraic semantics of substructural logics, where the multiplication is a conjunction and the residuals are implications.
Further reading
About this page
| Tag | E337A6WVH3 |
|---|---|
| URI | m2://E337A6WVH3 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06F05, 03G10 |
| Specializes | Lattice |
| Same as |
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