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Congruences and Green's relations on eventually regular semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

P. M. Edwards  and
T. E. Hall
P. M. Edwards
Affiliation:
Department of Econometrics, Monash University, Clayton, Victoria 3168, Australia
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Abstract

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A semigroup is eventually regular if each of its elements has some power that is regular. Let 𝓚 be one of Green's relations and let ρ be a congruence on an eventually regular semigroup S. It is shown for 𝓚 = 𝓛, 𝓡 and 𝓓 that if A and B are regular elements of S/ρ that are 𝓚-related in S/ρ then there exist elements a ∈ A, b ∈ B such that a and b are 𝓚-related in S. The result is not true for 𝓗 or 𝓙.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 1 , August 1987 , pp. 64 - 69
Copyright
Copyright © Australian Mathematical Society 1987

References

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[2]Edwards, P. M., ‘Eventually regular semigroups’, Bull. Austral. Math. Soc. 28 (1983), 23–38.CrossRefGoogle Scholar
[3]Hall, T. E., ‘Congruences and Green's relations on regular semigroups’, Glasgow Math. J. 13 (1972), 167–175.Google Scholar
[4]Rhodes, J., ‘Some results on finite semigroups’, J. Algebra 4 (1966), 471–504.Google Scholar