## Integral involutive FL-algebras

Abbreviation: IInFL

### Definition

An integral involutive FL-algebra or integral involutive residuated lattice is an involutive residuated lattice that is

integral: $x\vee 1 = 1$

##### Morphisms

Let $\mathbf{A}$ and $\mathbf{B}$ be involutive residuated lattices. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x \vee y)=h(x) \vee h(y)$, $h(x \cdot y)=h(x) \cdot h(y)$, $h({\sim}x)={\sim}h(x)$ and $h(1)=1$.

Example 1:

### Properties

Classtype Value Decidable 1) No $\infty$ Yes Yes No

### Finite members

$\begin{array}{lr} f(1)= &1\\ f(2)= &1\\ f(3)= &1\\ f(4)= &3\\ f(5)= &3\\ \end{array}$ $\begin{array}{lr} f(6)= &12\\ f(7)= &17\\ f(8)= &78\\ f(9)= &\\ f(10)= &\\ \end{array}$

### Superclasses

Involutive FL-algebras supervariety