Inverse semigroups with zero: covers and their structure
Sydney Bulman‐Fleming, John Fountain, Victoria A. R. Gould · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1999
Abstract We obtain analogues, in the setting of semigroups with zero, of McAlister's convering theoren and the structure theorems of McAlister, O'Carroll, and Margolis and Pin. The covers come from a classCof semigroups defined by modifying one of the many characterisations ofE-unitary inverse semigroups, namely, that an inverse semigroups isE-unitary if and only if it is an inverse image of an idempotent-pure homomorphism onto a group. The classCis properly contained in the class of allE*-unitary inverse semigroups introduced by Szendrei but properly contains the class of strongly categoricalE*-unitary semigroups recently considered by Gomes and Howie.