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

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)

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Clifford semigroup. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Clifford_semigroup&oldid=64292"