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

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

References

  1. ^ 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)
  2. ^ Algebraic characterizations of inverse semigroups and strongly regular rings theorem 2 (accessed on 14 December 2014)


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