Almost factorisable inverse semigroups

Abstract

In [3], McAlister introduced a class of semigroups, calledcovering semigroups, which were shown to play an important role in the theory ofE-unitary covers of semigroups. Strangely, this class of semigroups appears to have received little attention subsequently. It is the aim of this paper to rehabilitate them and to study their properties in more detail. As a first step, we have chosen to rename themalmost factorisable semigroups, since they can be regarded as the semigroup analogues of factorisable inverse monoids. Before discussing the contents of this paper in more detail we recall some standard terminology.