Cancellation and embedding theorems for compact uniquely divisible semigroups
type: Item
instance of: scholarly article
title: Cancellation and embedding theorems for compact uniquely divisible semigroups
zbMATH Open document ID: 0930.22003
DOI: 10.1007/BF03325433
author: Kirk Benningfield
published in: Semigroup Forum
publication date: 2000-02-07T00:00:00Z
review text: The author discusses conditions on a compact connected uniquely divisible semigroup \(S\) with trivial groups to have the property that the complement of the minimal ideal is cancellative. If \(x\in S\), then \([x]\) is the minimal uniquely divisible subsemigroup of \(S\) containing \(x\). For such a semigroup \(S\), these are known to have a trivial minimal ideal (zero). The zero of \([q]\) is denoted \(e_q\) and the core of an idempotent \(e\in S\) is defined \(\text{core}(e)=\{ x\in S: xe=e=ex\}\). The author defines a map \(\psi: S\rightarrow \text{core}(e_q)\) and proves that it is a continuous homomorphism. Consequently he selects \(u,v,q\in S\) which yields an important structural embedding of \(S\) into \([u][v]\times \text{core}(e_q)\).
reviewed by: John A. Hildebrant
Mathematics Subject Classification ID: 22A15
zbMATH DE Number: 1309710
zbMATH Keywords: topological semigroup
zbMATH Keywords: uniquely divisible semigroup
zbMATH Keywords: compact connected semigroup
zbMATH Keywords: cancellative
zbMATH Keywords: idempotent
zbMATH Keywords: minimal ideal
zbMATH Keywords: core
zbMATH Keywords: thread
zbMATH Keywords: embedding
zbMATH Keywords: topologically isomorphic
zbMATH Keywords: trivial groups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1309710