Abbreviation: GPEAlg

A \emph{generalized pseudo-effect algebra} is a generalized separation algebra that is

\emph{postive}: $x\cdot y=e$ implies $x=e=y$.

Let $\mathbf{A}$ and $\mathbf{B}$ be generalized pseudo-effect algebra. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(e)=e$ and if $x\cdot y\ne *$ then $h(x \cdot y)=h(x) \cdot h(y)$.

Example 1:

$\begin{array}{lr}

f(1)= &1\\
f(2)= &1\\
f(3)= &2\\
f(4)= &5\\
f(5)= &13\\
f(6)= &42\\
f(7)= &171\\
f(8)= &\\
f(9)= &\\
f(10)= &\\

\end{array}$

Generalized effect algebras

Generalized pseudo-orthoalgebras

Pseudo-effect algebras

Generalized separation algebras