Orthogonal sums of semigroups
type: Item
instance of: scholarly article
title: Orthogonal sums of semigroups
zbMATH Open document ID: 0828.20046
DOI: 10.1007/BF02783223
author: Stojan Bogdanović
author: Miroslav Ćirić
published in: Israel Journal of Mathematics
publication date: 1996-01-10T00:00:00Z
review text: A subset \(A\) of a semigroup \(S\) with zero is called 0-consistent if for every \(x, y \in S\), \(xy \in A\setminus \{0\}\) implies \(x, y \in A\). Every semigroup with zero is an orthogonal sum of orthogonal indecomposable semigroups and the set of all 0-consistent ideals is a complete Boolean algebra whose atoms are summands in the greatest orthogonal decomposition of the semigroup.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M12
zbMATH DE Number: 784928
zbMATH Keywords: orthogonal indecomposable semigroups
zbMATH Keywords: 0-consistent ideals
zbMATH Keywords: orthogonal decomposition
reviewed by: Jaak Henno
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 784928