Commutators and central extensions in universal algebra
type: Item
instance of: scholarly article
title: Commutators and central extensions in universal algebra
zbMATH Open document ID: 1020.08003
DOI: 10.1016/S0022-4049(02)00170-6
author: Marino Gran
published in: Journal of Pure and Applied Algebra
publication date: 2003-02-05T00:00:00Z
review text: Any congruence-modular variety \(V\) is equipped with a good theory of commutators. This makes it possible to define abelian objects and central extensions in \(V\). These concepts are classical for the variety of groups. The paper proves that central extensions defined in this way coincide with the categorical central extensions [cf. \textit{G. Janelidze} and \textit{G. M. Kelly}, ``Central extensions in universal algebra: A unification of three notions'', Algebra Univers. 44, 123-128 (2000; Zbl 1013.08009)] with respect to the full subcategory of abelian objects. The author uses the categorical approach to the theory of commutators suggested by \textit{G. Janelidze} and \textit{M. C. Pedicchio} [``Pseudogroupoids and commutators'', Theory Appl. Categ. 8, 408-456 (2001; Zbl 1008.18006)].
reviewed by: Jiří Rosický
Mathematics Subject Classification ID: 08B10
Mathematics Subject Classification ID: 18B40
zbMATH DE Number: 1864809
zbMATH Keywords: commutator
zbMATH Keywords: congruence-modular variety
zbMATH Keywords: groupoid
zbMATH Keywords: central extension
zbMATH Keywords: abelian objects
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1864809