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A note on congruences on orthodox semigroups

Published online by Cambridge University Press:  18 May 2009

D. B. McAlister
D. B. McAlister
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, U.S.A.
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C. Eberhart and W. Williams [3] showed that the least inverse semigroup congruence , on an orthodox semigroup S, plays a very important role in determining the structure of the lattice of congruences on S. In this note we show that their results can be applied to give an explicit construction for the idempotent separating congruences on S in terms of idempotent separating congruences on S/.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 1 , January 1985 , pp. 25 - 30
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

REFERENCES

1.Blyth, T. S. and McFadden, R. B., Unit orthodox semigroups, Glasgow Math. J. 24 (1983), 39–42.CrossRefGoogle Scholar
2.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vols. 1 and 2 (American Mathematical Society, 1961 and 1967).Google Scholar
3.Eberhart, C. and Williams, W., Congruences on an orthodox semigroup via the minimum inverse semigroup congruence, Glasgow Math. J. 18 (1977), 181–192.CrossRefGoogle Scholar
4.Hall, T. E., On regular semigroups whose idempotents form a subsemigroup, Bull. Austral. Math. Soc. 1 (1969), 195–208.CrossRefGoogle Scholar
5.Howie, J. M., Introduction to Semigroups (Academic Press, 1976).Google Scholar
6.McAlister, D. B., Groups, semilattices and inverse semigroups II, Trans. Amer. Math. Soc. 192 (1974), 351–370.CrossRefGoogle Scholar
7.McFadden, R. B., Unit orthodox semigroups, to appear.Google Scholar
8.Meakin, J., Congruences on orthodox semigroups, J. Austral. Math. Soc. 12 (1971), 323–341.CrossRefGoogle Scholar
9.Munn, W. D., A certain sublattice of the lattice of congruences on a regular semigroup, Proc. Cambridge Philos. Soc. 60 (1964), 385–391.CrossRefGoogle Scholar
10.Reilly, N. R. and Scheiblich, H. E., Congruences on regular semigroups, Pacific J. Math. 23 (1967), 349–360.CrossRefGoogle Scholar