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On Closed Ideals of βG

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Abstract

For every discrete group G, the Stone-Cech compactification βG has a natural structure of a right topological semigroup. Using the concept of Boolean group ideal on G, we propose a way of constructing closed ideals of the semigroup βG. In particular, we show that, for every infinite Abelian group G of cardinality κ, there are \(2^{2^{\kappa}}\) distinct closed ideals in βG.

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Authors and Affiliations

  1. Department of Cybernetics, Kyiv National University, Volodimirska 64, Kiev 01033, Ukraine

    I.V. Protasov & O.I. Protasova

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  1. I.V. Protasov
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  2. O.I. Protasova
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Correspondence to I.V. Protasov or O.I. Protasova.

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Protasov, I., Protasova, O. On Closed Ideals of βG. Semigroup Forum 75, 237–240 (2007). https://doi.org/10.1007/s00233-006-0650-1

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  • DOI: https://doi.org/10.1007/s00233-006-0650-1

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