[Home]Completely regular semigroups

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Abbreviation: CompRSgrp

Definition

A completely regular semigroup is a structure S = (S,·,−1) such that
· is associative:   (xy)z = x(yz),
−1 is an inverse:   xx−1x = x  and  (x−1)−1 = x and
xx−1 = x−1x.

Morphisms

Let S and T be completely regular semigroups. A morphism from S to T is a function h : ST that is a homomorphism: h(xy) = h(x)h(y)  and  h(x−1) = h(x)−1.

Some results

Examples

Properties

Classtype Variety
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 No
Definable principal congruences
Equationally definable principal congruences No
Amalgamation property
Strong amalgamation property
Epimorphisms are surjective

Finite members

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

Subclasses

Clifford semigroups
Bands
[Commutative completely regular semigroups]?

Superclasses

Regular semigroups


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Last edited April 18, 2003 8:50 pm (diff)
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