Hostname: page-component-7b7567c8c-lpg2g Total loading time: 0 Render date: 2026-11-15T10:24:59.513Z Has data issue: false hasContentIssue false
  • English
  • Français

Inverse semigroups as extensions of semilattices

Published online by Cambridge University Press:  18 May 2009

Liam O'Carroll
Liam O'Carroll
Affiliation:
The Mathematical Institute, Edinburgh EH1 1HZ
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.

Let S be an inverse semigroup with semilattice of idempotents E, and let ρ be a congruence on S. Then ρ is said to be idempotent-determined [2], or I.D. for short, if (a, b) ∈ р and a∈E imply that b ∈ E. If, further, ρ is a group congruence, then clearly ρ is the minimum group congruence on S, and in this case S is said to be proper [8]. Let T = S/ρ.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 1 , March 1975, pp. 12 - 21
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vols. I and II, Math. Surveys of the American Math. Soc. 7 (Providence, R.I., 1961 and 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.McAlister, D. B., Groups, semilattices and inverse semigroups II, Trans. Amer. Math. Soc.; to appear.Google Scholar
4.O'Carroll, L., A class of congruences on a posemigroup, Semigroup Forum 3 (1971), 173–179.CrossRefGoogle Scholar
5.O'Carroll, L., Reduced inverse and partially ordered semigroups, J. London Math. Soc. (I), 9 (1974), 293–301.CrossRefGoogle Scholar
6.O'Carroll, L., Embedding theorems for proper inverse semigroups, J. of Algebra; submitted.Google Scholar
7.Reilly, N. R., Inverse semigroups of partial transformations and θ-classes, Pac. J. Math. 41 (1972), 215–235.CrossRefGoogle Scholar
8.Saito, T., Proper ordered inverse semigroups, Pac. J. Math. 15 (1965), 649–666.Google Scholar
9.Schein, B. M., Completions, translational hulls, and ideal extensions of inverse semigroups, Czech. Math. J. 23 (98) (1973), 575–610.CrossRefGoogle Scholar