A Munn tree type representation for the elements of the bifree locally inverse semigroup

Abstract

The Munn tree representation for the elements of the free inverse monoid is an elegant and useful tool in the theory of inverse semigroups. It has been the starting point for many of the subsequent developments in this theory. In the present paper we generalize this representation for the elements of the bifree locally inverse semigroup. We will represent each element of the bifree locally inverse semigroup as an undirected tree whose vertices, called blocks, are special vertex-labeled graphs themselves. Another distinctive characteristic of these graphs is that they have different types of edges.