Ideals of ultrafilters on the collection of finite subsets of an infinite set
type: Item
instance of: scholarly article
title: Ideals of ultrafilters on the collection of finite subsets of an infinite set
zbMATH Open document ID: 1125.22002
author: Arthur D. Grainger
published in: Semigroup Forum
publication date: 2007-01-26T00:00:00Z
review text: 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.
reviewed by: Boris M. Schein
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 06B30
zbMATH DE Number: 5118911
MaRDI profile type: Publication
full work available at URL: s00233-006-0632-3
OpenAlex ID: W2019521721
DOI: 10.1007/S00233-006-0632-3
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description: scientific article; zbMATH DE number 5118911