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## Cancellative residuated lattices

Abbreviation: **CanRL**

### Definition

A ** cancellative residuated lattice** is a
residuated lattice
$\mathbf{L}=\langle L, \vee, \wedge, \cdot, e, \backslash, /\rangle$ such that

$\cdot$ is right-cancellative: $xz=yz\Longrightarrow x=y$

$\cdot$ is left-cancellative: $zx=zy\Longrightarrow x=y$

##### Morphisms

Let $\mathbf{L}$ and $\mathbf{M}$ be cancellative residuated lattices. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\rightarrow M$ that is a homomorphism:

$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$ $h(x\cdot y)=h(x)\cdot h(y)$, $h(x\backslash y)=h(x)\backslash h(y)$, $h(x/y)=h(x)/h(y)$ and $h(e)=e$

### Examples

Example 1:

### Basic results

### Properties

### Finite members

$\begin{array}{lr} None \end{array}$

\hyperbaseurl{http://math.chapman.edu/structures/files/}

### Subclasses

### Superclasses

### References

Trace: » cancellative_residuated_lattices