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On closed ideals of \(\beta G\). (English) Zbl 1127.22002

Summary: For every discrete group \(G\), the Stone-Čech compactification \(\beta G\) 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 \(\beta G\). In particular, we show that, for every infinite Abelian group \(G\) of cardinality \(\kappa \), there are \(2^{2^{\kappa}}\) distinct closed ideals in \(\beta G\).

MSC:

22A15 Structure of topological semigroups
20M12 Ideal theory for semigroups
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