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Inverse semigroups all of whose proper homomorphic images are groups

Published online by Cambridge University Press:  17 April 2009

Ralph P. Tucci
Affiliation:
Department of Mathematics and Computer Science, Loyola University New Orleans, New Orleans, LA.70118, United States of America, e-mail: [email protected]
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We characterise those inverse semigroups whose proper(non-isomorphic) homomorphic images are all groups. We also show that the bicyclic semigroup is the only such semigroup in certain cases.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Bernstein, N., ‘Group-like semigroups’, Semigroup Forum 3 (1971/1972), 5863.CrossRefGoogle Scholar
[2]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, (Vol. I) (American Mathematical Socociety, Providence, 1961).Google Scholar
[3]Fortunatov, V.A., ‘Congruences on simple extensions of semigroups’, Semigroup Forum 13 (1976/1977), 283295.CrossRefGoogle Scholar
[4]Goberstein, S.M., ‘Fundamental order relations on inverse semigroups and on their generalizations’, Semigroup Forum 21 (1980), 285328.CrossRefGoogle Scholar
[5]Jensen, B.A., ‘Infinite semigroups whose non-trivial homomorphs are all isomorphic’, Pacific J. Math 29 (1969), 583591.CrossRefGoogle Scholar
[6]Kowol, G. and Mitsch, H., ‘Nilpotent inverse semigroups with central idempotents’, Trans. Amer. Math. Soc. 271 (1982), 437449.CrossRefGoogle Scholar
[7]Lawson, M.V., Inverse semigroups (World Scientific, New Jersey, 1998).CrossRefGoogle Scholar
[8]Munn, W.D., ‘Congruence-free inverse semigroups’, Quart. J. Math. Oxford 2 (1974), 463484.CrossRefGoogle Scholar
[9]Petrich, M., Inverse semigroups (John Wiley and Sons, New York, 1984).Google Scholar
[10]Petrich, M., ‘Congruences on simple ω-semigroups’, Glasgow Math. J. 20 (1979), 87101.CrossRefGoogle Scholar
[11]Putcha, M.S., ‘Commutative semigroups whose homomorphic images in groups are groups’, Semigroup Forum 3 (1971/1972), 5157.CrossRefGoogle Scholar
[12]Reilly, N.R., ‘Congruence-free inverse semigroups’, Proc. London Math. Soc. 3 (1976), 497514.CrossRefGoogle Scholar
[13]Schein, B., ‘Pseudosimple commutative semigroups’, Monatsh. Math. 91 (1981), 7778.CrossRefGoogle Scholar
[14]Tamura, T., ‘Review of groups-like semigroups ≠2054’, by N. Bernstein, Mathematical Reviews 45 (1973), 373.Google Scholar
[15]Tamura, T. and Hamilton, H., ‘Commutative semigroups with greatest group- homomorphism’, Proc. Japan Acad. 47 (1971), 671675.Google Scholar
[16]Warne, R.J., ‘Congruences on ωn-bisimple semigroups’, J. Austral. Math. Soc. 9 (1969), 257274.CrossRefGoogle Scholar
[17]Zhu, P., ‘On Rees congruence semigroups’, Northeast. Math. J. 8 (1992), 185191.Google Scholar