Free inverse semigroups
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- by H. E. Scheiblich PDF
- Proc. Amer. Math. Soc. 38 (1973), 1-7 Request permission
Abstract:
At least three authors have offered proofs of the existence of a free inverse semigroup, but without describing its structure. This paper shows that if $X$ is a nonempty set, $G$ is the group on $X$, and $E$ is a certain subsemilattice of the power set of $G$, then a certain collection of principal ideal isomorphisms of $E$ is a free inverse semigroup on $X$.References
- A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR 0132791
- Carl Eberhart and John Selden, One-parameter inverse semigroups, Trans. Amer. Math. Soc. 168 (1972), 53–66. MR 296197, DOI 10.1090/S0002-9947-1972-0296197-4
- D. B. McAlister, A homomorphism theorem for semigroups, J. London Math. Soc. 43 (1968), 355–366. MR 224730, DOI 10.1112/jlms/s1-43.1.355
- A. G. Kurosh, The theory of groups, Chelsea Publishing Co., New York, 1960. Translated from the Russian and edited by K. A. Hirsch. 2nd English ed. 2 volumes. MR 0109842 V. V. Vagner, Generalized heaps and generalized groups with the transitive relation of compatibility, Učen. Zap. Saratov. Gos. Univ. Ser. Meh-Mat. 70 (1961), 25-39. (Russian)
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 1-7
- DOI: https://doi.org/10.1090/S0002-9939-1973-0310093-1
- MathSciNet review: 0310093