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Table of Contents

Commutative residuated lattices

Abbreviation: CRL

Definition

A \emph{commutative residuated lattice} is a residuated lattice L=L,,,,e,,/ such that

is commutative: xy=yx

Remark:

Morphisms

Let L and M be commutative residuated lattices. A morphism from L to M is a function h:LM that is a homomorphism:

h(xy)=h(x)h(y), h(xy)=h(x)h(y), h(xy)=h(x)h(y), h(xy)=h(x)h(y), h(x/y)=h(x)/h(y), and h(e)=e

Examples

Example 1:

Basic results

Properties

Finite members

f(1)=1f(2)=1f(3)=3f(4)=16f(5)=100f(6)=794f(7)=7493f(8)=84961

Subclasses

Commutative distributive residuated lattices

FLe-algebras

Superclasses

Commutative multiplicative lattices

Commutative residuated join-semilattices

Commutative residuated meet-semilattices

Residuated lattices

References