Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-15T17:40:17.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Inverse semigroups all of whose proper homomorphic images are groups

Published online by Cambridge University Press:  17 April 2009

Ralph P. Tucci
Ralph P. Tucci
Affiliation:
Department of Mathematics and Computer Science, Loyola University New Orleans, New Orleans, LA.70118, United States of America, e-mail: tucci@loyno.edu
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 3 , June 2004 , pp. 395 - 401
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Bernstein, N., ‘Group-like semigroups’, Semigroup Forum 3 (1971/1972), 58–63.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), 283–295.CrossRefGoogle Scholar
[4]Goberstein, S.M., ‘Fundamental order relations on inverse semigroups and on their generalizations’, Semigroup Forum 21 (1980), 285–328.CrossRefGoogle Scholar
[5]Jensen, B.A., ‘Infinite semigroups whose non-trivial homomorphs are all isomorphic’, Pacific J. Math 29 (1969), 583–591.CrossRefGoogle Scholar
[6]Kowol, G. and Mitsch, H., ‘Nilpotent inverse semigroups with central idempotents’, Trans. Amer. Math. Soc. 271 (1982), 437–449.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), 463–484.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), 87–101.CrossRefGoogle Scholar
[11]Putcha, M.S., ‘Commutative semigroups whose homomorphic images in groups are groups’, Semigroup Forum 3 (1971/1972), 51–57.CrossRefGoogle Scholar
[12]Reilly, N.R., ‘Congruence-free inverse semigroups’, Proc. London Math. Soc. 3 (1976), 497–514.CrossRefGoogle Scholar
[13]Schein, B., ‘Pseudosimple commutative semigroups’, Monatsh. Math. 91 (1981), 77–78.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), 671–675.Google Scholar
[16]Warne, R.J., ‘Congruences on ωn-bisimple semigroups’, J. Austral. Math. Soc. 9 (1969), 257–274.CrossRefGoogle Scholar
[17]Zhu, P., ‘On Rees congruence semigroups’, Northeast. Math. J. 8 (1992), 185–191.Google Scholar