\(\alpha\)-inflatable semigroups
type: Item
instance of: scholarly article
title: \(\alpha\)-inflatable semigroups
zbMATH Open document ID: 0759.22008
DOI: 10.1007/BF02574330
published in: Semigroup Forum
publication date: 1992-06-28T00:00:00Z
full work available at URL: https://eudml.org/doc/135135
review text: Let \(S\) be a discrete semigroup. Then the multiplication of \(S\) extends uniquely to the Stone-Čech compactification \(\beta S\), such that \(\beta S\) becomes a right topological semigroup with dense topological center. In an earlier paper the author has shown that if \(S\) is `inflatable', (i.e. \(S\) is countable, right cancellative, and satisfies a weak (but complicated) left cancellation law) then the product \((\beta S\setminus S)^ 2\) of the remainder \(\beta S\setminus S\) with itself does not contain the closure of the minimal ideal \(M(\beta S)\) of \(\beta S\). In the present paper the author extends this result to the newly defined class of `\(\alpha\)-inflatable semigroups' where \(\alpha\) is an integer \(\geq 2\) (the old `inflatable' is equivalent to 2-inflatable). For every \(\alpha\geq 2\) he constructs a semigroup which is \(\alpha+1\)- inflatable, but not \(\alpha\)-inflatable.
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 34208
zbMATH Keywords: \(\alpha\)-inflatable semigroups
zbMATH Keywords: discrete semigroup
zbMATH Keywords: Stone-Čech compactification
zbMATH Keywords: topological semigroup
zbMATH Keywords: remainder
zbMATH Keywords: minimal ideal
author: Hanson M. Umoh
reviewed by: Wolfgang A. F. Ruppert
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 34208