Contributions to the theory of O-simple inverse semigroups.

Abstract

The structure of O-bisimple and bisimple inverse semigroups has been extensively studied and established by Clifford, Reilly, Warne, Munn and McAlister. The initial work was done by Clifford in [0] on bisimple inverse semigroups with an identity and this was generalised by Reilly and Clifford in [13]. In [5] McAlister has produced a structure theorem for O-bisimple inverse semigroups in terms of groups and semilattices which can be specialised to give most of the previously known results in this area. These include the result of Munn described in [10] and the result of Reilly in [12], which deals with bisimple inverse semigroups whose semilattices are order isomorphic to the non negative integers with the reverse of the natural ordering, i.e. semilattices which are w-chains. Warne has made a study of those bisimple inverse semigroups whose semilattices are order isomorphic to the integers with the reverse of the natural ordering and has obtained in [14] a structure for these which ties closely with [12].