A classification of the maximal idempotent-generated subsemigroups of finite singular semigroups
type: Item
instance of: scholarly article
title: A classification of the maximal idempotent-generated subsemigroups of finite singular semigroups
zbMATH Open document ID: 0999.20052
author: Xiuliang Yang
author: Taijie You
published in: Semigroup Forum
publication date: 2002-05-30T00:00:00Z
review text: Let \(T_n\) be the full transformation semigroup on a set \(X_n\) of \(n\) letters, i.e., the set of all maps \(\alpha\colon X_n\to X_n\) under the operation of composition. For \(1\leq r\leq n\), let \(K(n,r)=\{\alpha\in T_n:|\text{im}(\alpha)|\leq r\}\). Each \(K(n,r)\) is a two-sided ideal of \(T_n\), and \(K(n,n-1)\) is the singular subsemigroup of \(T_n\). Various properties of \(K(n,n-1)\) are known. Among other things, it is well known that the singular subsemigroup is idempotent-generated. The authors calculate the number of and completely classify the maximal idempotent-generated subsemigroups of \(K(n,n-1)\).
reviewed by: Huang Wenxue
Mathematics Subject Classification ID: 20M20
zbMATH DE Number: 1747979
zbMATH Keywords: classification
zbMATH Keywords: full transformation semigroups
zbMATH Keywords: idempotents
zbMATH Keywords: idempotent-generated subsemigroups
zbMATH Keywords: singular subsemigroups
MaRDI profile type: Publication
full work available at URL: s002330010096
OpenAlex ID: W1996582729
DOI: 10.1007/S002330010096
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description: scientific article; zbMATH DE number 1747979