88:"While there is an abundance of natural examples of inverse semigroups, for completely regular semigroups the examples (beyond completely simple semigroups) are mostly artificially constructed: the minimum ideal of a finite semigroup is completely simple, and the various relatively free completely regular semigroups are the other more or less natural examples."
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was the first to publish a major paper on completely regular semigroups though he used the terminology "semigroups admitting relative inverses" to refer to such semigroups. The name "completely regular semigroup" stems from Lyapin's book on semigroups. In the
Russian literature, completely regular
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of these groups. Hence completely regular semigroups are also referred to as "unions of groups".
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semigroups are often called "Clifford semigroups". In the
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generalize this notion and their class includes all completely regular semigroups.
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of completely regular semigroups forms an important subclass of the
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Clifford, A. H. (1941). "Semigroups admitting relative inverses".
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125:(4). American Mathematical Society: 1037–1049.
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61:. In a completely regular semigroup, each
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254:Fundamentals of semigroup theory
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229:Completely regular semigroups
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231:. Wiley-IEEE. p. 65.
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72:and the semigroup is the
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32:of the semigroup. The
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119:Annals of Mathematics
301:Algebraic structures
162:E S Lyapin (1963).
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18:mathematics
295:Categories
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164:Semigroups
104:References
268:(Chap. 4)
78:Epigroups
26:semigroup
92:See also
84:Examples
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149:1968781
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