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Free completely regular semigroups

Published online by Cambridge University Press:  18 May 2009

P. G. Trotter
P. G. Trotter
Affiliation:
University of Tasmania, Hobart Tasmania, Australia
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A completely regular semigroup is a semigroup that is a union of groups. The aim here is to provide an alternative characterization of the free completely regular semigroup Fcrx on a set X to that given by J. A. Gerhard in [3, 4].

Although the structure theory for completely regular semigroups was initiated in 1941 [1] by A. H. Clifford it was not until 1968 that it was shown by D. B. McAlister [5] that Fcrx exists. More recently, in [7], M. Petrich demonstrated the existence of Fcrx by showing that completely regular semigroups form a variety of unary semigroups (that is, semigroups with the additional operation of inversion).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 2 , July 1984 , pp. 241 - 254
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

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