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#### Abbreviation: CompRSgrp

### Definition

A *completely regular semigroup* is a structure *S* = (*S*,·,^{−1}) such that

· is associative: (*x**y*)*z* = *x*(*y**z*),

^{−1} is an inverse: *x**x*^{−1}*x* = *x* and (*x*^{−1})^{−1} = *x* and

*x**x*^{−1} = *x*^{−1}*x*.

### Morphisms

Let *S* and *T* be completely regular semigroups. A morphism from
*S* to *T* is a function *h* : *S*→*T* that is a
homomorphism:
*h*(*x**y*) = *h*(*x*)*h*(*y*) and *h*(*x*^{−1}) = *h*(*x*)^{−1}.

### Some results

### Examples

### Properties

### Finite members

[Size 1]?: 1

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### Subclasses

Clifford semigroups

Bands

[Commutative completely regular semigroups]?

### Superclasses

Regular semigroups