Orderings of the Stone-Čech remainder of a discrete semigroup
type: Item
instance of: scholarly article
title: Orderings of the Stone-Čech remainder of a discrete semigroup
zbMATH Open document ID: 0934.22011
DOI: 10.1016/S0166-8641(98)00073-X
author: Neil Hindman
author: Salvador Garcia-Ferreira
author: D. Strauss
published in: Topology and its Applications
publication date: 2000-04-17T00:00:00Z
review text: The multiplication \(\cdot\) in a discrete semigroup \((S,\cdot)\) extends to the Stone-Čech compactification \(\beta S\) of \(S\), thus defining a right topological semigroup \((\beta S,*)\). The authors study the Rudin-Keisler order and the recently defined Comfort order in \(\beta S\setminus S\). It turns out that the two orders have quite a different nature. For example, the set of Comfort predecessors of an element \(p\in \beta S\setminus S\) is a subsemigroup of \(\beta S\), while this always fails to be true for an arbitrary cancellative semigroup \(S\). It is also shown in the paper that the two orders reveal a number of algebraic properties of the semigroup \((\beta S,*)\).
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 54D40
Mathematics Subject Classification ID: 54D80
zbMATH DE Number: 1367521
zbMATH Keywords: Rudin-Keisler order
zbMATH Keywords: Comfort order
zbMATH Keywords: discrete semigroup
zbMATH Keywords: subsemigroup
zbMATH Keywords: cancellative semigroup
zbMATH Keywords: ultrafilter
zbMATH Keywords: Stone-Čech compactification
zbMATH Keywords: right topological semigroup
reviewed by: Mikhail Tkachenko
MaRDI profile type: Publication
full work available at URL: s0166-8641(98)00073-x
OpenAlex ID: W2034051639
description: scientific article; zbMATH DE number 1367521