### Table of Contents

## Separation algebras

Abbreviation: **SepAlg**

### Definition

A \emph{separation algebra} is a generalized separation algebra such that

$\cdot$ is \emph{commutative}: $x\cdot y = y\cdot x$.

I.e., a separation algebra is a cancellative commutative partial monoid.

##### Morphisms

Let $\mathbf{A}$ and $\mathbf{B}$ be cancellative partial monoids. 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

### Finite members

$\begin{array}{lr}

f(1)= &1\\ f(2)= &2\\ f(3)= &3\\ f(4)= &8\\ f(5)= &13\\ f(6)= &39\\ f(7)= &120\\ f(8)= &507\\ f(9)= &\\ f(10)= &\\

\end{array}$