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On difunctionality of class relations

2020-03Journal article Open access
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dc.contributor.authorHoefnagel, Michael
dc.contributor.authorJanelidze, Zurab
dc.contributor.authorRodelo, Diana
dc.date.accessioned2021-06-24T11:35:48Z
dc.date.available2021-06-24T11:35:48Z
dc.date.issued2020-03
dc.description.abstractFor a given variety V of algebras, we define a class relation to be a binary relation R subset of S(2)which is of the form R = S-2 boolean AND K for some congruence class K on A(2), where A is an algebra in V such that S subset of A. In this paper we study the following property of V : every reflexive class relation is an equivalence relation. In particular, we obtain equivalent characterizations of this property analogous to well-known equivalent characterizations of congruence-permutable varieties. This property determines a Mal'tsev condition on the variety and in a suitable sense, it is a join of Chajda's egg-box property as well as Duda's direct decomposability of congruence classes.
dc.description.sponsorshipSouth African National Research FoundationNational Research Foundation - South Africa
dc.description.sponsorshipCentre for Mathematics of the University of Coimbra - Portuguese Government through FCT/MEC [UID/MAT/00324/2019]
dc.description.sponsorshipEuropean Regional Development Fund through the Partnership Agreement PT2020
dc.description.versioninfo:eu-repo/semantics/publishedVersion
dc.identifier.doi10.1007/s00012-020-00651-z
dc.identifier.issn0002-5240
dc.identifier.urihttp://hdl.handle.net/10400.1/16538
dc.language.isoeng
dc.peerreviewedyes
dc.publisherSpringer
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectClass relations
dc.subjectCongruence permutability
dc.subjectCongruence distributivity
dc.subjectCongruence modularity
dc.subjectDirectly decomposable congruence classes
dc.subjectDifunctionality
dc.subjectEgg-box property
dc.subjectMal'tsev condition
dc.subjectMal'tsev variety
dc.subjectShifting lemma
dc.subject.otherMathematics
dc.titleOn difunctionality of class relations
dc.typejournal article
dspace.entity.typePublication
oaire.citation.issue2
oaire.citation.startPage19
oaire.citation.titleAlgebra Universalis
oaire.citation.volume81
person.familyNameRodelo
person.givenNameDiana
person.identifier.ciencia-id6C16-FCF9-64A0
person.identifier.orcid0000-0002-4816-3234
person.identifier.ridAFH-8267-2022
person.identifier.scopus-author-id8216708900
rcaap.rightsopenAccess
rcaap.typearticle
relation.isAuthorOfPublication311bbe08-1f8a-4c84-87e7-23ddd55c89a3
relation.isAuthorOfPublication.latestForDiscovery311bbe08-1f8a-4c84-87e7-23ddd55c89a3

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