Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] L. M. Gluskin, Elementary generalized groups, Mat. Sb. 41 (83) (1957), 23-36. (Russian) MR 19, 836. MR 0090595 (19:836e)
  • [3] D. B. McAlister, A homomorphism theorem for semigroups, J. London Math. Soc. 43 (1968), 355-366. MR 37 #329. MR 0224730 (37:329)
  • [4] N. R. Reilly and H. E. Scheiblich, Congruences on regular semigroups, Pacific J. Math. 23 (1967), 349-360. MR 36 #2725. MR 0219646 (36:2725)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20M10

Retrieve articles in all journals with MSC: 20M10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0296197-4
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

American Mathematical Society