Clifford semigroup

A Clifford semigroup (sometimes also called "inverse Clifford semigroup") is a completely regular inverse semigroup.

It is an inverse semigroup with[http://www-circa.mcs.st-and.ac.uk/Theses/cacmsc.pdf Presentations of Semigroups and Inverse Semigroups] {{webarchive|url=https://web.archive.org/web/20061011032525/http://www-circa.mcs.st-and.ac.uk/Theses/cacmsc.pdf |date=2006-10-11 }} section 4.3 Some Results on Clifford Semigroups (accessed on 14 December 2014)

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

In a Clifford semigroup,[https://gentzen.wordpress.com/2014/12/06/algebraic-characterizations-of-inverse-semigroups-and-strongly-regular-rings/ Algebraic characterizations of inverse semigroups and strongly regular rings] theorem 2 (accessed on 14 December 2014) $xy=yx\; \backslash leftrightarrow\; x^\{-1\}y=yx^\{-1\}$.