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An example involving a non-regular -class in a semigroup

Published online by Cambridge University Press:  09 April 2009

T. E. Hall
T. E. Hall
Affiliation:
Monash UniversityClayton, Victoria
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We answer in the negative (by considering an example) the problem posed in exercise 6 of § 2.3, page 62 [1], namely: If a D-class D of a semigroup S is a subsemigroup of S, then is D necessarily bisimple? For any semigroup T, we let LT, RT, HT, DT and JT denote Green's relations on T.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 3 , May 1972 , pp. 257 - 258
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups (Math. Surveys, number 7, Amer. Math. Soc., Vol. I 1961).Google Scholar
[2]Clark, W. E., ‘Remarks on the kernel of a matrix semigroup’, Czechoslovak Math. J. 15 (1965) 305–310.CrossRefGoogle Scholar