Binary homomorphisms and natural dualities
type: Item
instance of: scholarly article
title: Binary homomorphisms and natural dualities
zbMATH Open document ID: 0996.08004
DOI: 10.1016/S0022-4049(01)00059-7
published in: Journal of Pure and Applied Algebra
publication date: 2002-06-24T00:00:00Z
review text: One of the most important questions in the theory of natural dualities is: ``Which finite algebras are dualisable?'' In connection with this question, the authors investigate ways in which certain binary homomorphisms of a finite algebra can guarantee its dualisability (of particular interest are those binary homomorphisms which are lattice, flat-semilattice or group operations). They prove that a finite algebra which has a pair of lattice operations amongst its binary homomorphisms is dualisable; as an application of this result, they find that every finite unary algebra can be embedded into a dualisable algebra. Also they develop some general tools that are used to prove the dualisability of a large number of unary algebras (for example is proved that the endomorphisms of a finite cyclic group are the operations of a dualisable unary algebra).
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 08A60
zbMATH DE Number: 1758367
zbMATH Keywords: finite algebras
zbMATH Keywords: binary homomorphisms
zbMATH Keywords: lattice operations
zbMATH Keywords: unary algebra
zbMATH Keywords: dualisable algebra
zbMATH Keywords: finite cyclic group
author: David M. Clark
author: Brian A. Davey
author: Jane G. Pitkethly
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
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full work available at URL: s0022-4049(01)00059-7
OpenAlex ID: W2084778066
description: scientific article; zbMATH DE number 1758367