Cancellative semigroups

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(xy) = h(x)h(y).

Some results

Examples

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

Properties

Classtype	Quasivariety
Equational theory
Quasiequational theory
First-order theory
Locally finite	No
Residual size
Congruence distributive	No
Congruence modular	No
Congruence n-permutable	No
Congruence regular	No
Congruence uniform	No
Congruence extension property
Definable principal congruences
Equationally definable principal congruences	No
Amalgamation property	No
Strong amalgamation property	No
Epimorphisms are surjective	No

Finite members

[Size 1]?: 1
[Size 2]?:
[Size 3]?:
[Size 4]?:
[Size 5]?:
[Size 6]?:
[Size 7]?:

Subclasses

Cancellative monoids

Superclasses

Semigroups