Geodesic
Free completely regular semigroups
Glasgow mathematical journal, Tome 25 (1984) no. 2, pp. 241-254

Voir la notice de l'article provenant de la source Cambridge University Press

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). 
Trotter, P. G. Free completely regular semigroups. Glasgow mathematical journal, Tome 25 (1984) no. 2, pp. 241-254. doi: 10.1017/S0017089500005668
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[1] 1.Clifford, A. H., Semigroups admitting relative inverses, Ann. of Math. (2) 42 (1941), 1037–1049. Google Scholar | DOI

[2] 2.Clifford, A. H., The free completely regular semigroup on a set, J. Algebra 59 (1979), 434–451. Google Scholar | DOI

[3] 3.Gerhard, J. A., Free completely regular semigroups I: Representation, J. Algebra 82 (1983), 135–142. Google Scholar | DOI

[4] 4.Gerhard, J. A., Free completely regular semigroups II: Word problem, J. Algebra 82 (1983), 143–156. Google Scholar | DOI

[5] 5.McAlister, D. B., A homomorphism theorem for semigroups, J. London Math. Soc. 43 (1968), 355–366. Google Scholar | DOI

[6] 6.Petrich, M., The structure of completely regular semigroups, Trans. Amer. Math. Soc. 189 (1974), 211–236. Google Scholar | DOI

[7] 7.Petrich, M., Certain varieties and quasivarieties of completely regular semigroups, Canad. J. Math. 29 (1977), 1171–1197. Google Scholar | DOI

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