Clifford Semigroup

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

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

References

↑ Presentations of Semigroups and Inverse Semigroups 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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[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)