generalized_pseudo-effect_algebras

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=====Generalized pseudo-effect algebras=====

Abbreviation: **GPEAlg**

====Definition====
A \emph{generalized pseudo-effect algebra} is a [[generalized separation algebra]] that is

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

==Morphisms==
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 $h(x \cdot y)=h(x) \cdot h(y)$.

====Examples====
Example 1: 

====Basic results====


====Properties====

^[[Classtype]]                        |first-order  |
^[[Equational theory]]                | |
^[[Quasiequational theory]]           | |
^[[First-order theory]]               | |
^[[Locally finite]]                   | |
^[[Residual size]]                    | |
^[[Congruence distributive]]          | |
^[[Congruence modular]]               | |
^[[Congruence $n$-permutable]]        | |
^[[Congruence regular]]               | |
^[[Congruence uniform]]               | |
^[[Congruence extension property]]    | |
^[[Definable principal congruences]]  | |
^[[Equationally def. pr. cong.]]      | |
^[[Amalgamation property]]            | |
^[[Strong amalgamation property]]     | |
^[[Epimorphisms are surjective]]      | |

====Finite members====

$\begin{array}{lr}
  f(1)= &1\\
  f(2)= &1\\
  f(3)= &2\\
  f(4)= &5\\
  f(5)= &13\\
  f(6)= &42\\
  f(7)= &171\\
  f(8)= &\\
  f(9)= &\\
  f(10)= &\\
\end{array}$

====Subclasses====
[[Generalized effect algebras]]

[[Generalized pseudo-orthoalgebras]]

[[Pseudo-effect algebras]]

====Superclasses====
[[Generalized separation algebras]]


====References====

Trace: • linear_logic_algebras • notation_and_terminology

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