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Characterization of finite amenable transformation semigroups: corrigendum

Published online by Cambridge University Press:  09 April 2009

C. O. Wilde
C. O. Wilde
Affiliation:
Naval Postrgaduate SchoolMonterey California, 93940, U.S.A.
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Theorem 6 of Wilde (1971) is in error. Følner's condition is necessary, but not sufficient, for amenability of a τ-semigroup. For clearly sufficiency would imply that every finite τ-semigroup is amenable, and the simple example on p. 503 of Wilde (1971) shows that this is not so. We refer the reader to Namioka (1964) for a lucid explanation of the fundamental ideas involved.

Type
Corrigendum
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 3 , May 1975 , pp. 384
Copyright
Copyright © Australian Mathematical Society 1975

References

Namioka, I. (1964), ‘Føners's condition for amenable semigroups’, Math. Scand. 15, 18–28.CrossRefGoogle Scholar
Wilde, C. (1973), ‘Characterization of finite amenabled transformation semigroups’, J. Ausral Math. Soc. 15, 86–93.CrossRefGoogle Scholar
Wilde, C., Jayachandran, T. (1971), ‘Amenable transformation semigroups’, J. Austral. Math. Soc. 12, 502–510.CrossRefGoogle Scholar