Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-20T06:37:08.167Z Has data issue: false hasContentIssue false
  • English
  • Français

Certain congruences on a completely regular semigroup

Published online by Cambridge University Press:  18 May 2009

Thomas L. Pirnot
Thomas L. Pirnot
Affiliation:
Kutztown State College, Kutztown, Pennsylvania 19530, U.S.A.
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.

Congruences on a semigroup S such that the corresponding factor semigroups are of a special type have been considered by several authors. Frequently it has been difficult to obtain worthwhile results unless restrictions have been imposed on the type of semigroup considered. For example, Munn [6] has studied minimum group congruences on an inverse semigroup, R. R. Stoll [9] has considered the maximal group homomorphic image of a Rees matrix semigroup which immediately determines the smallest group congruence on a Rees matrix semigroup. The smallest semilattice congruence on a general or commutative semigroup has been studied by Tamura and Kimura [10], Yamada [12] and Petrich [8]. In this paper we shall study congruences ρ on a completely regular semigroup S such that S/ρ is a semilattice of groups. We shall call such a congruence an SG-congruence.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 15 , Issue 2 , September 1974 , pp. 109 - 120
Copyright
Copyright © Glasgow Mathematical Journal Trust 1974

References

REFERENCES

1.Clifford, A. H., Semigroups admitting relative inverses,Ann. of Math. 42 (1941), 1037–1049.CrossRefGoogle Scholar
2.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vols. I and II, Amer. Math. Soc. Mathematical Surveys, No. 7 (Providence, R. I., 1961, 1967).Google Scholar
3.Howie, J. M. and Lallement, G., Certain fundamental congruences on a regular semigroup, Proc. Glasgow Math. Assoc. 7 (1966), 145–159.CrossRefGoogle Scholar
4.Lallement, G., Congruences et équivalences de Green sur un demi groupe régulier, C. R. Acad. Sci. Paris 262 (1966), 613–616.Google Scholar
5.Ljapin, E. S., Semigroups, English translation (revised edition) (Amer. Math. Soc, Providence, R. I., 1968).Google Scholar
6.Munn, W. D., A class of irreducible matrix representations of an arbitrary inverse semigroup, Proc. Glasgow Math. Assoc. 5 (1961), 41–48.CrossRefGoogle Scholar
7.Petrich, M., Introduction to semigroups (Columbus, Ohio, 1973).Google Scholar
8.Petrich, M., The maximal semilattice decomposition of a semigroup, Math. Zeit. 85 (1954), 68–82.CrossRefGoogle Scholar
9.Stoll, R. R., Homomorphisms of a semigroup onto a group, Amer. J. Math. 73 (1951), 475–481.CrossRefGoogle Scholar
10.Tamura, T. and Kimura, N., On decompositions of a commutative semigroup, Kodai Math. Sem. Rep. 4 (1954), 109–112.Google Scholar
11.Thierrin, G., Contribution à la theorie des anneaux et des demi-groupes, Comment. Math. Helv. 32 (1957), 93–112.CrossRefGoogle Scholar
12.Yamada, M., On the greatest semilattice decomposition of a semigroup, Kodai Math. Sem. Rep. 7 (1955), 59–62.CrossRefGoogle Scholar