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The closure of the smallest ideal of an ultrafilter semigroup

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Abstract

Let S be a discrete semigroup, let β S be the Stone-Čech compactification of S, and let T be a closed subsemigroup of β S. We characterize ultrafilters from the smallest ideal K(T) of T and from its closure c ℓ  K(T). We show that, for a large class of closed subsemigroups of β S, c ℓ  K(T) is not an ideal of T. This class includes the subsemigroups 0+⊂βℝ d and ℍ κ ⊂β(⊕ κ ℤ2).

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Authors and Affiliations

  1. School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, 2050, South Africa

    Onesmus Shuungula, Yevhen Zelenyuk & Yuliya Zelenyuk

Authors
  1. Onesmus Shuungula
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  2. Yevhen Zelenyuk
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  3. Yuliya Zelenyuk
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Corresponding author

Correspondence to Yevhen Zelenyuk.

Additional information

Communicated by Jimme D. Lawson.

The second and the third authors were supported by NRF grants FA2007041200005 and IFR2008041600015, respectively, and The John Knopfmacher Centre for Applicable Analysis and Number Theory.

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Shuungula, O., Zelenyuk, Y. & Zelenyuk, Y. The closure of the smallest ideal of an ultrafilter semigroup. Semigroup Forum 79, 531–539 (2009). https://doi.org/10.1007/s00233-009-9173-x

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  • DOI: https://doi.org/10.1007/s00233-009-9173-x

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