An Invitation to C-semigroups

Semigroups with an additional unary operation called a (right) closure are investigated. These ``closure semigroups'' may be viewed as (not necessarily regular) generalisations of inverse semigroups, and several powerful structural aspects of inverse semigroup theory are shown to extend naturally to some important classes of closure semigroups. These include representations as partial transformations on sets, natural partial orders that are multiplication (and closure) respecting, and simple descriptions of some important congruences.