Geodesic
An embedding theorem for free inverse semigroups
Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 217-222

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In this note it is shown that if S is a free inverse semigroup of rank at least two and if e, f are idempotents of S such that e > f then S can be embedded in the partial semigroup eSe/fSf. The proof makes use of Scheiblich's construction for free inverse semigroups [7, 8] and of Reilly's characterisation of a set of free generators in an inverse semigroup [4, 5]. 
Munn, W. D. An embedding theorem for free inverse semigroups. Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 217-222. doi: 10.1017/S0017089500004687
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