Birkhoff's variety theorem in many sorts
type: Item
instance of: scholarly article
title: Birkhoff's variety theorem in many sorts
zbMATH Open document ID: 1257.08003
author: Jiří Adámek
author: Jiří Rosický
author: E. M. Vitale
published in: Algebra Universalis
publication date: 2012-11-27T00:00:00Z
review text: In this paper, Birkhoff's characterization of equational classes is proved to generalize the case of finitely many sorts: For every set \(S\) of sorts and every \(S\)-sorted signature \(\Sigma\), the equational classes of \(\Sigma\)-algebras are precisely the full subcategories of \(\Sigma\)-Alg closed under products, subalgebras, regular quotients,and directed unions. For infinitely sorted algebras, closure under directed unions needs to be added.
reviewed by: Radomír Halaš
Mathematics Subject Classification ID: 08A68
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 08C05
zbMATH DE Number: 6110488
zbMATH Keywords: many-sorted algebras
zbMATH Keywords: Birkhoff variety theorem
MaRDI profile type: Publication
full work available at URL: s00012-012-0185-0
OpenAlex ID: W2101082039
cites work: Q4293501
cites work: Q3164468
cites work: Q3221381
cites work: Q4002149
DOI: 10.1007/S00012-012-0185-0
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description: scientific article; zbMATH DE number 6110488