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Strongly E-reflexive inverse semigroups

Published online by Cambridge University Press:  20 January 2009

L. O'Carroll
L. O'Carroll
Affiliation:
Department of MathematicsThe King's BuildingsEdinburgh, EH9 3J2
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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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 4 , September 1977 , pp. 339 - 354
Copyright
Copyright © Edinburgh Mathematical Society 1977

References

REFERENCES

(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).Google Scholar
(2) Green, D. G., Extensions of a Semilattice by an inverse semigroup, Bull. Austral. Math. Soc. 9 (1973), 21–31.CrossRefGoogle Scholar
(3) Hardy, D. W. and Tirasupa, Y., Semilattices of proper inverse semigroups, Semigroup Forum 13 (1976), 29–36.CrossRefGoogle Scholar
(4) McAlister, D. B., Groups, semilattices and inverse semigroups II, Trans. Amer. Math. Soc. 196 (1974), 351–369.CrossRefGoogle Scholar
(5) McFadden, R. and O'Carroll, L., F-inverse semigroups, Proc. London Math. Soc. 22 (1971), 652–666.CrossRefGoogle Scholar
(6) Munn, W. D., A class of irreducible matrix representations of an arbitrary inverse semigroup, Proc. Glasgow Math. Assoc. 5 (1961), 41–48.CrossRefGoogle Scholar
(7) Munn, W. D., Uniform semilattices and bisimple inverse semigroups, Quart. J. Math. Oxford (2) 17 (1966), 151–159.CrossRefGoogle Scholar
(8) Munn, W. D. and Reilly, N. R., Congruences on a bisimple tu-semigroup, Proc. Glasgow Math. Assoc. 7 (1966), 184–192.CrossRefGoogle Scholar
(9) Munn, W. D. and Reilly, N. R., E-unitary congruences on inverse semigroups, Glasgow Math. J. 17 (1976), 57–75.Google Scholar
(10) O'Carroll, L., Reduced inverse and partially ordered semigroups, J. London Math. Soc. (2) 9 (1974), 293–301.CrossRefGoogle Scholar
(11) O'Carroll, L., Inverse semigroups as extensions of semilattices, Glasgow Math. J. 16 (1975), 12–21.CrossRefGoogle Scholar
(12) O'Carroll, L., Idempotent determined congruences on inverse semigroups, Semigroup Forum 12 (1976), 233–243.CrossRefGoogle Scholar
(13) Petrich, M., Introduction to Semigroups (Merrill, Columbus, Ohio, 1973).Google Scholar
(14) Reilly, N. R., Extensions of congruences and homomorphisms to translational hulls, Pacific J. Math. 54 (1974), 209–228.CrossRefGoogle Scholar
(15) Saito, T., Proper ordered inverse semigroups, Pacific J. Math. 15 (1965), 649–666.CrossRefGoogle Scholar
(16) Vagner, V. V., Theory of generalised heaps and generalised groups, Matem. Sbornik (NS) 32 (1953), 545–632.Google Scholar