Sums of idempotents in \(\beta{}\mathbb{N}\)
type: Item
instance of: scholarly article
title: Sums of idempotents in \(\beta{}\mathbb{N}\)
zbMATH Open document ID: 0759.22004
DOI: 10.1007/BF02574328
author: John F. Berglund
author: Neil Hindman
published in: Semigroup Forum
publication date: 1992-06-28T00:00:00Z
full work available at URL: https://eudml.org/doc/135133
review text: Let + also indicate the continuous extension to \(\beta\mathbb{N}\) of addition on \(\mathbb{N}\). The structure theorem for compact semigroups tells us that the sum \(p+q\) of two idempotents in the same minimal left (or right) ideal of \(\beta\mathbb{N}\) is also an idempotent. Here the authors address the question: is the sum \(p+q\) of minimal idempotents an idempotent only in this situation? In their main result they find a family \(\{p_ \gamma\mid \gamma < 2^ c\}\) of minimal idempotents such that \(p_ \gamma+p_ \mu\) and \(p_ \mu+p_ \gamma\) are not idempotent whenever \(\gamma < \mu < 2^ c\).
reviewed by: Paul Milnes
Mathematics Subject Classification ID: 22A15
zbMATH DE Number: 34206
zbMATH Keywords: sums of idempotents
zbMATH Keywords: Stone-Čech compactification
zbMATH Keywords: set of positive integers
zbMATH Keywords: topological semigroup
zbMATH Keywords: minimal idempotents
MaRDI profile type: Publication
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OpenAlex ID: W2022969231
description: scientific article; zbMATH DE number 34206