Bosets and fundamental semigroups

Speaker: Brad Roberts, University of Sydney

Abstract: Part of the classical theory of inverse semigroups includes the construction of all fundamental inverse semigroups from semilattices which is due to Munn (1966). This has been generalised to the construction of all fundamental regular semigroups by Hall (1973), Nambooripad (1974) and Grillet (1974). Recently Patrick Jordan (2002) has studied a construction of a semigroup T_E from any (not necessarily regular) boset E. In the case where E is regular it reproduces all the other constructions up to isomorphism. We will discuss the regular case as well as some new results for some non regular semigroups.