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#### Abbreviation: CanSgrp

### Definition

A *cancellative semigroup* is a semigroup *S* = (*S*,·) such that
· is left cancellative: *z*·*x* = *z*·*y* ⇒ *x* = *y* and

· is right cancellative: *x*·*z* = *y*·*z* ⇒ *x* = *y*.

### Morphisms

Let *S* and *T* be cancellative semigroups. A morphism from
*S* to *T* is a function *h* : *S*→*T* that is a
homomorphism:
*h*(*x**y*) = *h*(*x*)*h*(*y*).

### Some results

### Examples

(**N**, + ), the natural numbers, with additition.

### Properties

### Finite members

[Size 1]?: 1

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### Subclasses

Cancellative monoids

### Superclasses

Semigroups