Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-08T06:28:19.567Z Has data issue: false hasContentIssue false
  • English
  • Français

Congruences induced by transitive representations of inverse semigroups

Published online by Cambridge University Press:  18 May 2009

Mario Petrich  and
Stuart Rankin
Mario Petrich
Affiliation:
University of Western Ontario, London, Canada
Stuart Rankin
Affiliation:
University of Western Ontario, London, Canada
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.

Transitive group representations have their analogue for inverse semigroups as discovered by Schein [7]. The right cosets in the group case find their counterpart in the right ω-cosets and the symmetric inverse semigroup plays the role of the symmetric group. The general theory developed by Schein admits a special case discovered independently by Ponizovskiǐ [4] and Reilly [5]. For a discussion of this topic, see [1, §7.3] and [2, Chapter IV].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 1 , January 1987 , pp. 21 - 40
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. II (Amer. Math. Soc., 1967).Google Scholar
2.Petrich, M., Inverse semigroups (Wiley-Interscience, 1984).Google Scholar
3.Petrich, M. and Rankin, S., Certain properties of congruences on inverse semigroups (submitted).Google Scholar
4.Ponizovskiǐ, I. S., On representations of inverse semigroups by partial one-to-one transformations, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 989–1002.Google Scholar
5.Reilly, N. R., Contributions to the theory of inverse semigroups (Doctoral Dissertation, University of Glasgow, 1965).Google Scholar
6.Scheiblich, H. E., Concerning congruences on symmetric inverse semigroups, Czechoslovak Math J. 23 (1973), 1–10.CrossRefGoogle Scholar
7.Schein, B. M., Representations of generalized groups, Izu. Vyssh. Uchebn. Zaved. Mat. 3 (1962), 164–176.Google Scholar