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    O'Carroll, L. 1978. Strongly E-reflexive inverse semigroups II. Proceedings of the Edinburgh Mathematical Society, Vol. 21, Issue. 01, p. 1.
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Strongly E-reflexive inverse semigroups

  • L. O'Carroll (a1)
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Let S be an inverse semigroup with semilattice of idempotents E. We denote by σ the minimum group congruence on S (6), and by τ the maximum idempotent-determined congruence on S (2). (Recall that the congruence η on S is called idempotent-determined if (e, x)∈ η and e ∈ E imply that x ∈ E.) In general τ ⊆ σ.

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COPYRIGHT: © Edinburgh Mathematical Society 1977
References
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(1) Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups (Math. Surveys No. 7, Amer. Math. Soc, Providence, Vol. 1,1961 and Vol. 2, 1967).
(2) Green, D. G., Extensions of a Semilattice by an inverse semigroup, Bull. Austral. Math. Soc. 9 (1973), 21–31.
(3) Hardy, D. W. and Tirasupa, Y., Semilattices of proper inverse semigroups, Semigroup Forum 13 (1976), 29–36.
(4) McAlister, D. B., Groups, semilattices and inverse semigroups II, Trans. Amer. Math. Soc. 196 (1974), 351–369.
(5) McFadden, R. and O'Carroll, L., F-inverse semigroups, Proc. London Math. Soc. 22 (1971), 652–666.
(6) Munn, W. D., A class of irreducible matrix representations of an arbitrary inverse semigroup, Proc. Glasgow Math. Assoc. 5 (1961), 41–48.
(7) Munn, W. D., Uniform semilattices and bisimple inverse semigroups, Quart. J. Math. Oxford (2) 17 (1966), 151–159.
(8) Munn, W. D. and Reilly, N. R., Congruences on a bisimple tu-semigroup, Proc. Glasgow Math. Assoc. 7 (1966), 184–192.
(9) Munn, W. D. and Reilly, N. R., E-unitary congruences on inverse semigroups, Glasgow Math. J. 17 (1976), 57–75.
(10) O'Carroll, L., Reduced inverse and partially ordered semigroups, J. London Math. Soc. (2) 9 (1974), 293–301.
(11) O'Carroll, L., Inverse semigroups as extensions of semilattices, Glasgow Math. J. 16 (1975), 12–21.
(12) O'Carroll, L., Idempotent determined congruences on inverse semigroups, Semigroup Forum 12 (1976), 233–243.
(13) Petrich, M., Introduction to Semigroups (Merrill, Columbus, Ohio, 1973).
(14) Reilly, N. R., Extensions of congruences and homomorphisms to translational hulls, Pacific J. Math. 54 (1974), 209–228.
(15) Saito, T., Proper ordered inverse semigroups, Pacific J. Math. 15 (1965), 649–666.
(16) Vagner, V. V., Theory of generalised heaps and generalised groups, Matem. Sbornik (NS) 32 (1953), 545–632.
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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
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