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] xx1=x1x. Examples of Clifford semigroups are groups and commutative inverse semigroups.

In a Clifford semigroup,[2] xy=yxx1y=yx1.

References

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  1. Presentations of Semigroups and Inverse Semigroups Script error: No such module "webarchive". 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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