Ideals of ultrafilters on the collection of finite subsets of an infinite set
Let \(I\) be the set of all nonempty finite subsets of an infinite set \(J\) and let \(\beta I\) be the set of all ultrafilters on \(I\). The Stone-Čech compactification of the join semilattice \((I,\cup)\) equipped with the discrete topology is a compact (Hausdorff) right topological semigroup denoted \((\beta I,\uplus)\). This semigroup was considered by the author [Semigroup Forum 67, 443--453 (2003; Zbl 1045.22002)] and \textit{S. Koppelberg} [Semigroup Forum 72, 63--74 (2006; Zbl 1111.22003)] who, in particular, studied \(K(\beta I)\), the Suschkewitsch kernel (that is, the least ideal) of \((\beta I,\uplus)\). The author continues these studies. He considers ideals of certain compact subsemigroups of \(\beta I\). His main result is too technical to be reproduced here.
scientific article; zbMATH DE number 5118911
scientific article