Clifford semigroup

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A Clifford semigroup (sometimes also called "inverse Clifford semigroup") is a completely regular inverse semigroup. It is an inverse semigroup with[1] xx−1=x−1x. Examples of Clifford semigroups are groups and commutative inverse semigroups.

In a Clifford semigroup,[2] xy=yx↔x−1y=yx−1.

References

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  1. ↑ Presentations of Semigroups and Inverse Semigroups Template:Webarchive section 4.3 Some Results on Clifford Semigroups (accessed on 14 December 2014)
  2. ↑ Algebraic characterizations of inverse semigroups and strongly regular rings theorem 2 (accessed on 14 December 2014)
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