Abbreviation: GPEAlg

A generalized pseudo-effect algebra is a generalized separation algebra that is

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