[Home]Cancellative semigroups

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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 : ST 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


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Last edited April 14, 2003 9:28 pm (diff)
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