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The maximum idempotent-separating congruence on a regular semigroup

Published online by Cambridge University Press:  20 January 2009

John Meakin
John Meakin
Affiliation:
The University of Nebraska, Lincoln, Nebraska 68508, U.S.A.
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It has been established by G. Lallement (3) that the set of idempotent-separating congruences on a regular semigroup S coincides with the set ∑() of congruences on S which are contained in Green's equivalence on S. In view of this and Lemma 10.3 of A. H. Clifford and G. B. Preston (1) it is obvious that the maximum idempotent-separating congruence on a regular semigroup S is given by

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 2 , December 1972 , pp. 159 - 163
Copyright
Copyright © Edinburgh Mathematical Society 1972

References

REFERENCES

(1) Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups (Math. Surveys, No. 7, Amer. Math. Soc, Vol. I, 1961, Vol II, 1967).Google Scholar
(2) Howie, J. M., The maximum idempotent-separating congruence on an inverse semigroup, Proc. Edinburgh Math. Soc. (2) 14 (1964–1965), 71–79.CrossRefGoogle Scholar
(3) Lallement, G., Demi-groupes reguliers, Ann. Mat. Pura Appl. (4) 77 (1967) 47–129.CrossRefGoogle Scholar
(4) Meakin, J. C., Congruences on orthodox semigroups, J. Austral. Math. Soc. 12 (1971), 323–341.Google Scholar