Clifford semigroup
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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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