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Idempotent-equivalent congruences on orthodox semigroups

Published online by Cambridge University Press:  09 April 2009

John Meakin
John Meakin
Affiliation:
Department of MathematicsMonash University Clayton, Victoria
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Any congruence on a semigroup S with a nonempty set Es of idempotents induces a partition of the set Es. Two congruences ρ and σ on the semigroup S are defined to be idempotent-equivalent congruences on S if ρ and σ induce the same partition of Es. In this paper we investigate idempotent-equivalent congruences on orthodox semigroups (regular semigroups in which the set of idempotents forms a subsemigroup).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 2 , May 1970 , pp. 221 - 241
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups (Math. Surveys, number 7, Amer. Math. Soc., Vol. I 1961, Vol. II 1967).Google Scholar
[2]Meakin, J. C., ‘Congruences on Orthodox Semigroups’, J. Australian Math. Soc. (to appear).Google Scholar
[3]Reilly, N. R. and Scheiblich, H. E., ‘Congruences on Regular Semigroups’, Pacific J. of Mathematics 23 (1967), 349–360.CrossRefGoogle Scholar