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Chains of congruences on a completely 0-simple semigroup

Published online by Cambridge University Press:  09 April 2009

G. B. Preston
G. B. Preston
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria.
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Let ρ and σ be two congruences on a completely 0-simple semigroup. Suppose that there is a maximal chain of congruences from ρ to σ which is of finite length. Then, as we shall show, any maximal chain of congruences from ρ to σ finite and of the same length.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 1 , February 1965 , pp. 76 - 82
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, volume I, Math. Surveys, No. 7, Amer. Math. Soc., 1961.Google Scholar
[2]Preston, G. B., Congruences on completely 0-simple semigroups, Proc. London Math. Soc., 11 (1961), 557–576.Google Scholar
[3]Rees, D., On semigroups, Proc. Cambridge Phil. Soc., 36 (1940), 387–400.Google Scholar