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A '''Clifford semigroup''' (sometimes also called "inverse Clifford semigroup") is a [[completely regular semigroup|completely regular]] [[inverse semigroup]].
It is an inverse semigroup with
<math>xx^{-1}=x^{-1}x</math>. Examples of Clifford semigroups are groups and commutative inverse semigroups.

In a Clifford semigroup, <math> xy=yx \leftrightarrow x^{-1}y=yx^{-1}</math>.

[[Category:Algebraic structures]]
[[Category:Semigroup theory]]