Algebraic coalitions
type: Item
instance of: scholarly article
title: Algebraic coalitions
zbMATH Open document ID: 0903.08012
published in: Algebra Universalis
publication date: 1998-11-23T00:00:00Z
review text: An algebra \(A\) is called abelian whenever the centre of \(A\) is equal to \(A\times A\). {SELF} denotes the category of all graphs \(\mathcal R\) that have exactly one object \(0_{\mathcal R}\), together with all graph maps between any two such graphs. The idea of an algebra in {SELF} is introduced in the paper. It is shown that such algebras are abelian with a one-element subalgebra in a congruence modular variety. This leads to the notion of algebraic coalition, which is characterized for congruence modular varieties and for varieties of Jónsson-Tarski algebras. Finally, the relationship among algebraic coalitions, Gumm difference term, and the centre of an algebra is studied.
Mathematics Subject Classification ID: 08B10
zbMATH DE Number: 1226223
zbMATH Keywords: abelian algebra
zbMATH Keywords: centre
zbMATH Keywords: coalition
zbMATH Keywords: congruence modular variety
zbMATH Keywords: Jónsson-Tarski algebras
zbMATH Keywords: Gumm difference term
author: Andrew Ensor
reviewed by: Jaromír Duda
MaRDI profile type: Publication
full work available at URL: s000120050035
OpenAlex ID: W4234069304
DOI: 10.1007/S000120050035
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description: scientific article; zbMATH DE number 1226223