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On the Rees-Suschkewitsch structure theorem

Published online by Cambridge University Press:  24 October 2008

John S. Pym
John S. Pym
Affiliation:
University of Reading
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Extract

It was remarked in (1) that many of the results valid for compact (this term is taken to imply Hausdorff) semigroups with jointly continuous multiplication also hold if the multiplication is only separately continuous. It is the purpose of this note to show that this is true of the structure theorem for compact simple semigroups. Any unsubstantiated facts about semigroups which we use may be found in the second section of (1) (the results given there do not depend on the assumption that a semigroup should contain an identity).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 3 , July 1963 , pp. 563 - 566
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Deleeuw, K., and Glicksberg, I., Applications of almost periodic compactifications. Acta Math. 105 (1961), 63–97.CrossRefGoogle Scholar
(2)Ellis, R., Locally compact transformation groups. Duke Math. J. 24 (1957), 119–126.CrossRefGoogle Scholar
(3)Pym, J. S., Idempotent measures on semigroups. Pacific J. Math. 12 (1962), 685–698.CrossRefGoogle Scholar
(4)Rees, D., On semi-groups. Proc. Cambridge Philos. Soc. 36 (1940), 387–400.CrossRefGoogle Scholar
(5)Suschkewitsch, A., Über die endliehen Gruppen ohne das Gesetz der eindeutigen Umkerbarkeit. Math. Ann. 99 (1928), 30–50.CrossRefGoogle Scholar
(6)Wallace, A. D., The Rees-Suschkewitsch structure theorem for compact simple semigroups. Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 430–432.CrossRefGoogle ScholarPubMed
(7)Clifford, A. H., Semigroups containing minimal ideals. American J. Math. 70 (1948), 521–526.CrossRefGoogle Scholar