Table of Contents
Cancellative commutative semigroups
Abbreviation: CanCSgrp
Definition
A \emph{cancellative commutative semigroup} is a commutative semigroup $\mathbf{S}=\langle S,\cdot \rangle $ such that
$\cdot $ is \emph{cancellative}: $x\cdot z=y\cdot z\Longrightarrow x=y$
Morphisms
Let $\mathbf{S}$ and $\mathbf{T}$ be cancellative commutative semigroups. A morphism from $\mathbf{S}$ to $\mathbf{T}$ is a function $h:S\rightarrow T$ that is a homomorphism:
$h(xy)=h(x)h(y)$
Examples
Example 1: $\langle \mathbb{N},+\rangle $, the natural numbers, with additition.
Basic results
Properties
Finite members
$\begin{array}{lr}
f(1)= &1
f(2)= &
f(3)= &
f(4)= &
f(5)= &
f(6)= &
f(7)= &
\end{array}$
