Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-04T20:10:28.758Z Has data issue: false hasContentIssue false
  • English
  • Français

Decompositions of the congruence lattice of a semigroup

Published online by Cambridge University Press:  20 January 2009

W. D. Munn
W. D. Munn
Affiliation:
Department of MathematicsUniversity of GlasgowGlasgow, G12 8QWScotland
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.

The purpose of this note is to extend the results of Reilly and Scheiblich (6) (see also Scheiblich (7) and Hall (2)) on the θ-class decomposition of the congruence lattice of a regular semigroup and, at the same time, to provide an alternative proof of these results.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 2 , June 1980 , pp. 193 - 198
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

REFERENCES

(1)Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Math. Surveys of the Amer. Math. Soc. 7 (Providence, R.I., 1961 (Vol. I) and 1967 (Vol. II)).Google Scholar
(2)Hall, T. E., On the lattice of congruences on a regular semigroup, Bull. Australian Math. Soc. 1 (1969), 231–235.Google Scholar
(3)Hall, T. E., Congruences and Green's relations on regular semigroups, Glasgow Math. J. 13 (1972), 167–175.CrossRefGoogle Scholar
(4)Howie, J. M., An introduction to semigroup theory, London Math. Soc. monographs 7 (London, 1976).Google Scholar
(5)Lallement, G., Congruences et équivalences de Green sur un demi-groupe régulier, C.R. Acad. Sc. 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