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Strongly E-reflexive inverse semigroups II

Published online by Cambridge University Press:  20 January 2009

L. O'Carroll
Affiliation:
Dept. of Mathematics, J.C.M.B., King's Buildings, Edinburgh, 9.
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In a recent paper (13), we introduced the class of strongly E-reflexive inversesemigroups. This class was shown to coincide with the class of those inverse semigroups which are semilattices of E-unitary inverse semigroups. In particular, therefore, E-unitary inverse semigroups and semilattices of groups are strongly E-reflexive, and in fact so are subdirect products of these two types of semigroups.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1978

References

REFERENCES

(1) Mills, J. E., Certain congruences on orthodox semigroups, Pacific J. Math. 64 (1976), 217226.CrossRefGoogle Scholar
(2) 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
(3) Coudron, A., Sur les extensions des demigroupes reciproques, Bull. Soc. Roy. Sci. Liege 37 (1968), 409419.Google Scholar
(4) D'Alarcao, H. D., Idempotent-separating extensions of inverse semigroups, J. Austral. Math. Soc. 9 (1969), 211217.CrossRefGoogle Scholar
(5) Green, D. G., Extensions of a semilattice by an inverse semigroup, Bull. Austral. Math. Soc. 9 (1973), 2131.CrossRefGoogle Scholar
(6) Hardy, D. W. and Tirasupa, Y., Semilattices of proper inverse semigroups, Semi- group Forum 13 (1976), 2936.CrossRefGoogle Scholar
(7) Howie, J. M., The maximum idempotent-separating congruence on an inverse semigroup, Proc. Edinburgh Math. Soc. (2) 14 (1964), 7179.CrossRefGoogle Scholar
(8) Lausch, H., Cohomology of inverse semigroups, J. Algebra 35 (1975), 273303.CrossRefGoogle Scholar
(9) Mcalister, D. B., Some covering and embedding theorems for inverse semigroups, J. Austral. Math. Soc, 22 (1976), 188211.CrossRefGoogle Scholar
(10) Munn, W. D., A class of irreducible matrix representations of an arbitrary inverse semigroup, Proc. Glasgow Math. Assoc. 5 (1961), 4148.CrossRefGoogle Scholar
(11) Munn, W. D. and Reilly, N. R., Congruences on a bisimple ω-semigroup, Proc. Glasgow Math. Assoc. 7 (1966), 184192.CrossRefGoogle Scholar
(12) O'Carroll, L., Reduced inverse and partially ordered semigroups, J. London Math. Soc. (2)9(1974), 293301.CrossRefGoogle Scholar
(13) O'Carroll, L., Strongly E-reflexive inverse semigroups, Proc. Edinburgh Math. Soc, (2) 20 (1977), 339354.CrossRefGoogle Scholar
(14) Petrich, M., Introduction to Semigroups, (Merrill, Columbus, Ohio, 1973).Google Scholar
(15) Tamura, T., The theory of construction of finite semigroups I, Osaka Math. J. 8 (1956), 243261Google Scholar