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

Presentations of Semigroups and Inverse Semigroups Archived 2006-10-11 at the Wayback Machine section 4.3 Some Results on Clifford Semigroups (accessed on 14 December 2014)
Algebraic characterizations of inverse semigroups and strongly regular rings theorem 2 (accessed on 14 December 2014)

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