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Kernels of orthodox semigroup homomorphisms

Published online by Cambridge University Press:  09 April 2009

Ruth Feigenbaum
Ruth Feigenbaum
Affiliation:
5 Northwestern Avenue, Butler, New Jersey 07405, U.S.A.
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Any congruence on an orthodox semigroup S induces a partition of the set E of idempotents of S satisfying certain normality conditions. Meakin (1970) has characterized those partitions of E which are induced by congruences on S as well as the largest congruence ρ and the smallest congruence σ on S corresponding to such a partition of E. In this paper a more precise description of ρ and σ is given.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 2 , September 1976 , pp. 234 - 245
Copyright
Copyright © Australian Mathematical Society 1976

References

Clifford, A. H. and Preston, G. B. (1961), The Algebraic Theory of Semigroups (Math. Surveys, No. 7, Amer. Math. Soc., Vol. I, 1961).Google Scholar
Howie, J. M. (1964), ‘The maximum idempotent-separating congruence on an inverse semigroup’, Proc. Edinburgh Math. Soc. 14, 71–79.CrossRefGoogle Scholar
Lallement, G. (1966), ‘Congruences et équivalences de Green sur un demi-groupe régulier’, C. R. Acad. Sci. Paris 262, 613–616.Google Scholar
Meakin, John (1971), ‘Idempotent-equivalent congruences on orthodox semigroups’, J. Austral. Math. Soc. 11, 221–241.CrossRefGoogle Scholar
Meakin, John (1971), ‘Congruences on orthodox semigroups’, J. Austral. Math. Soc. 12, 323–341.CrossRefGoogle Scholar
Reilly, N. R. and Scheiblich, H. E. (1967), ‘Congruences on regular semigroups’, Pacific J. Math. 23, 349–360.CrossRefGoogle Scholar
Scheiblich, H. E. (1974), ‘Kernels of inverse semigroup homomorphisms’, J. Austral. Math. Soc. 18, 289–292.CrossRefGoogle Scholar