Expansions , Free Inverse Semigroups , and Schiitzenberger Product
نویسنده
چکیده
In this paper we shall present a new constructron of the free inverse monoid on a set A’. Contrary to the prevrous constructions of 19, 111, our construction is symmetric and originates from classrcal ideas of language theory. The mgredlents of this construction are the free group on X and the relatron that associates to a word II’ of the free monoid on X, the set of all pairs (u, v) such that uu = rr It follows at once from our construction that the free inverse monoid on X can be naturally embedded into the Schltzenberger product of two free groups of basrs X. We shall also give some connections with the theory of expansions as developed by Rhodes and Bnget 12, 31. ‘(1’ 1987 Academic Press, Inc
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