Matrix relation algebras.
type: Item
instance of: scholarly article
title: Matrix relation algebras.
zbMATH Open document ID: 1058.03073
author: Mohamed El Bachraoui
author: Marcel van de Vel
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: The collection of all \(n\times n\) matrices with entries from a given relation algebra \(\mathcal R\) forms a relation algebra \(M_n(\mathcal R)\) with naturally defined operations. The paper contains lists of properties of \(\mathcal R\) (e.g.\ atomicity, simplicity, representability, non-embeddability, density, etc.) which are preserved also in \(M_n(\mathcal R)\). The authors introduce so-called \(M_n\)-algebras as relation algebras enriched with \(n-1\) constants and subject to suitable equational axioms. The main result is that for fixed \(n>0\), the class \(M_n(\mathcal R)\) for some \(\mathcal R\) coincides with the class of reducts of \(M_n\)-algebras and hence has a first-order characterization. As a consequence, homomorphic images and simple proper extensions of matrix relation algebras are isomorphic to matrix relation algebras.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 03G15
zbMATH DE Number: 2158810
zbMATH Keywords: first-order property
zbMATH Keywords: matrix relation algebra
zbMATH Keywords: relativization
MaRDI profile type: Publication
full work available at URL: s000120200001
OpenAlex ID: W1968811649
DOI: 10.1007/S000120200001
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description: scientific article; zbMATH DE number 2158810