One-parameter inverse semigroups
Authors:
Carl Eberhart and John Selden
Journal:
Trans. Amer. Math. Soc. 168 (1972), 53-66
MSC:
Primary 20M10
DOI:
https://doi.org/10.1090/S0002-9947-1972-0296197-4
MathSciNet review:
0296197
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Abstract | References | Similar Articles | Additional Information
Abstract: This is the second in a projected series of three papers, the aim of which is the complete description of the closure of any one-parameter inverse semigroup in a locally compact topological inverse semigroup. In it we characterize all one-parameter inverse semigroups. In order to accomplish this, we construct the free one-parameter inverse semigroups and then describe their congruences.
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A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vols. 1, 2, Math. Surveys, no. 7, Amer. Math. Soc., Providence, R. I., 1961, 1967. MR 24 #A2627; MR 36 #1558.
- L. M. Gluskin, Elementary generalized groups, Mat. Sb. N. S. 41(83) (1957), 23–36 (Russian). MR 0090595
- D. B. McAlister, A homomorphism theorem for semigroups, J. London Math. Soc. 43 (1968), 355–366. MR 224730, DOI https://doi.org/10.1112/jlms/s1-43.1.355
- N. R. Reilly and H. E. Scheiblich, Congruences on regular semigroups, Pacific J. Math. 23 (1967), 349–360. MR 219646
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Additional Information
Keywords:
Inverse semigroup,
one-parameter inverse semigroup,
bicyclic semigroup,
free semigroup,
lattice of congruences,
freely generated,
bisimple inverse semigroup,
Green’s relations,
normal congruence,
group congruence,
lattice of subgroups,
kernel
Article copyright:
© Copyright 1972
American Mathematical Society
