Abstract :
This paper is the first of two papers devoted to the study of amalgamated free products of inverse semigroups. The subject of our second paper is the structure of amalgamated free products while this one is concerned with offering concrete descriptions of normal forms. We define a lower bounded amalgam of inverse semigroups and present a procedure by which the Schützenberger automata of the amalgamated free product can be constructed. Those automata which can be such a Schützenberger automaton are characterized, yielding a canonical form for the amalgamated free product. Our proof makes use of the graph-theoretic ideas developed by Jones, Margolis, Meakin, and Stephen for presentations of inverse semigroups.
