Dualisability versus residual character: a theorem and a counterexample
type: Item
instance of: scholarly article
title: Dualisability versus residual character: a theorem and a counterexample
zbMATH Open document ID: 1119.08001
author: Jane G. Pitkethly
author: Ross Willard
author: Brian A. Davey
published in: Journal of Pure and Applied Algebra
publication date: 2007-06-26T00:00:00Z
review text: A finite algebra \(A\) is inherently non-dualisable if there is no natural representation for the quasivariety \(\text{ISP}(B)\), where \(B\) is a finite algebra such that \(A\in \text{ISP}(B)\). In this paper the authors show that a finite algebra must be inherently non-dualisable if the variety that it generates is both residually large and congruence meet-semidistributive. Also, they give the first example of a finite dualisable algebra that generates a variety that is residually large.
reviewed by: Florentina Chirteş
Mathematics Subject Classification ID: 08A05
Mathematics Subject Classification ID: 08B26
Mathematics Subject Classification ID: 06A12
zbMATH DE Number: 5167552
zbMATH Keywords: dualisability
zbMATH Keywords: variety
zbMATH Keywords: residual character
zbMATH Keywords: subdirectly irreducible algebras
MaRDI profile type: Publication
Wikidata QID: Q124793329
full work available at URL: j.jpaa.2006.10.001
OpenAlex ID: W2087543767
cites work: Q4220406
cites work: Standard topological algebras: syntactic and principal congruences and profiniteness
cites work: Natural dualities for quasivarieties generated by a finite commutative ring.
cites work: Near unanimity: An obstacle to general duality theory
cites work: Dualizability and graph algebras
cites work: Natural dualities for semilattice-based algebras
cites work: Dualisability of \(p\)-semilattices
cites work: Q3775604
cites work: Q3856954
cites work: DUALISABILITY OF FINITE SEMIGROUPS
cites work: Algebras Whose Congruence Lattices are Distributive.
cites work: Self-Rectangulating Varieties of Type 5
cites work: Full duality among graph algebras and flat graph algebras
cites work: Residually small varieties of semigroups
cites work: Residual smallness relativized to congruence types. I
cites work: Congruence Relations in Semi-Lattices
cites work: Dualisability. Unary algebras and beyond
cites work: Nilpotent groups are not dualizable
DOI: 10.1016/J.JPAA.2006.10.001
description: scientific article; zbMATH DE number 5167552