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## Cancellative semigroups

Abbreviation: **CanSgrp**

### Definition

A ** cancellative semigroup** is a semigroup $\mathbf{S}=\langle
S,\cdot\rangle$ such that

$\cdot $ is left cancellative: $z\cdot x=z\cdot y\Longrightarrow x=y$

$\cdot $ is right cancellative: $x\cdot z=y\cdot z\Longrightarrow x=y$

##### Morphisms

Let $\mathbf{S}$ and $\mathbf{T}$ be cancellative 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

$\begin{array}{lr} f(1)= &1\\ f(2)= &\\ f(3)= &\\ f(4)= &\\ f(5)= &\\ f(6)= &\\ f(7)= &\\ \end{array}$

\hyperbaseurl{http://math.chapman.edu/structures/files/}

### Subclasses

### Superclasses

### References

Trace: » cancellative_semigroups