Free inverse semigroups
Various methods have been given for establishing the existence of the free inverse semigroup FIA on a set A, and for constructing it explicitly (see, for example, , , , , , ). In this paper we outline a graph-theoretic technique for representing the elements of FIA. This depends on the notion, introduced here, of a word-tree on A. With the aid of this technique various properties of FIA are easily deduced: some of these are stated below.
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