Generalized Inflations of Completely Simple Semigroups
Qiang Wang, Shelly L. Wismath · Algebra Colloquium · 2007
Clarke and Monzo defined a construction called a generalized inflation of a semigroup, and proved that for unions of groups, all null extensions are generalized inflations. We characterize when a groupoid containing a completely simple semigroup B is an associative generalized inflation of B, and thus provide a way to construct all associative generalized inflations (null extensions) of a given completely simple semigroup. This answers a question posed by Clarke and Monzo.