Abstract
The purpose of this note is to give a characterization of a free inverse semigroup on a singleton set. It will be shown that if B is the bicyclic semigroup, then a certain inverse subsemigroup F of B × B is a free elementary inverse semigroup.
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References
Clifford, A.H. and G.B. Preston,The Algebraic Theory of Semigroups, Vol. 1, Amer. Math. Soc., Math Surverys No. 7, (Providence, R.I., 1961).
Eberhart, Carl and John Selden,One parameter inverse semigroups, Trans. Amer. Math. Soc., (to appear).
Gluskin, L.M.,Elementary inverse semigroups, Mat. Sbornik 83 (1957), 23–36.
McAlister, D.B.,A homomorphism theorem for semigroups, J. London Math. Soc. 43 (1968), 355–366.
Munn, W.D.,Uniform semilattices and bisimple inverse semigroups, Quart. J. Math. Oxford (2), 17 (1966), 151–159.
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Scheiblich, H.E. A characterization of a free elementary inverse semigroup. Semigroup Forum 2, 76–79 (1971). https://doi.org/10.1007/BF02572275
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DOI: https://doi.org/10.1007/BF02572275