Clifford semigroup

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^{-1}x. Examples of Clifford semigroups are groups and commutative inverse semigroups.

In a Clifford semigroup,[2] xy=yx \leftrightarrow x^{-1}y=yx^{-1}.

References

  1. ↑ Presentations of Semigroups and Inverse Semigroups 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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