Abbreviation: GMV
A \emph{generalized MV-algebra} is a residuated lattices $\mathbf{L}=\langle L,\vee, \wedge, \cdot, e, \backslash, /\rangle$ such that
$x\vee y=x/(y\backslash x\wedge e)$, $x\vee y=(x/y\wedge e)\backslash y$
Let $\mathbf{L}$ and $\mathbf{M}$ be generalized MV-algebras. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\rightarrow M$ that is a homomorphism:
$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$, $h(x\backslash y)=h(x)\backslash h(y)$, $h(x/y)=h(x)/h(y)$, $h(e)=e$
Example 1:
$\begin{array}{lr}
f(1)= &1
f(2)= &1
f(3)= &
f(4)= &
f(5)= &
f(6)= &
\end{array}$