Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T14:23:06.236Z Has data issue: false hasContentIssue false
  • English
  • Français

On the lattice of congruences on an eventually regular semigroup

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

P. M. Edwards
P. M. Edwards
Affiliation:
Department of Econometrics Monash UniversityClayton, VictoriaAustralia3168
Rights & Permissions [Opens in a new window]

Abstract

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.

A natural equivalence θ on the lattice of congruences λ(S) of a semigroup S is studied. For any eventually regular semigroup S, it is shown that θ is a congruence, each θ-class is a complete sublattice of λ(S) and the maximum element in each θ-class is determined. 1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 2 , April 1985 , pp. 281 - 286
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Birkhoff, Garrett, Lattice theory, Amer. Math. Soc. Colloq. Publ., Vol. 25, Amer. Math. Soc., Providence, R. I., 1964.Google Scholar
[2]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Math. Surveys No. 7, Amer. Math. Soc., Providence, R. I., Vol. I, 1961; Vol. II, 1967.Google Scholar
[3]Edwards, P. M., ‘Eventually regular semigroups’, Bull. Austral. Math. Soc. 28 (1983), 23–38.CrossRefGoogle Scholar
[4]Hall, T. E., ‘On the lattice of congruences on a regular senngroup’, Bull. Austral. Math. Soc. 1 (1969), 231–235.CrossRefGoogle Scholar
[5]Lallement, Gérard, ‘Congruences et équivalences de Green sur un demi-groupe régulier’, C. R. Acad. Sci. Paris Sér. A 262 (1966), 613–616.Google Scholar
[6]Reilly, N. R. and Scheiblich, H. E., ‘Congruences on regular semigroups’, Pacific J. Math. 23 (1967), 349–360.CrossRefGoogle Scholar
[7]Scheiblich, H. E., ‘Certain congruence and quotient lattices related to completely 0-simple and primitive regular semigroups’, Glasgow Math. J. 10 (1969), 21–24.CrossRefGoogle Scholar