Clifford semigroup

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

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

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)

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