Abbreviation: CliffSgrp
A \emph{Clifford semigroup} is an inverse semigroups $\mathbf{S}=\langle S,\cdot,^{-1}\rangle $ that is also completely regular semigroups.
A \emph{Clifford semigroup} is a structure $\mathbf{S}=\langle S,\cdot,^{-1}\rangle $ such that
$\cdot$ is associative: $(xy)z=x(yz)$
$^{-1}$ is an inverse: $xx^{-1}x=x$, $(x^{-1})^{-1}=x$
$xx^{-1}=x^{-1}x$, $xx^{-1}y^{-1}y=y^{-1}yxx^{-1}$, $xx^{-1}=x^{-1}x$
Let $\mathbf{S}$ and $\mathbf{T}$ be Clifford semigroups. A morphism from $\mathbf{S}$ to $\mathbf{T}$ is a function $h:S\rightarrow T$ that is a homomorphism:
$h(xy)=h(x)h(y)$, $h(x^{-1})=h(x)^{-1}$
Example 1:
$\begin{array}{lr}
f(1)= &1
f(2)= &
f(3)= &
f(4)= &
f(5)= &
f(6)= &
f(7)= &
\end{array}$