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Reconstructing Classical Algebras via Ternary Operations

2025-04-25Journal article Open access
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datacite.subject.fosEngenharia e Tecnologia
datacite.subject.sdg09:Indústria, Inovação e Infraestruturas
datacite.subject.sdg12:Produção e Consumo Sustentáveis
dc.contributor.authorPereira Fatelo, Jorge
dc.contributor.authorMartins-Ferreira, Nelson
dc.date.accessioned2025-07-31T15:24:00Z
dc.date.available2025-07-31T15:24:00Z
dc.date.issued2025-04-25
dc.descriptionArticle number - 1407
dc.descriptionThis article belongs to the Section A: Algebra and Logic
dc.description.abstractAlthough algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified using ternary operations. In this context, we introduce structures that contain two constants and a ternary operation. We demonstrate that these structures are isomorphic to various significant algebraic systems, including Boolean algebras, de Morgan algebras, MV-algebras, and (near-)rings of characteristic two. Our work highlights the versatility of ternary operations in describing and connecting diverse algebraic structures.eng
dc.description.sponsorshipThis research work was supported by the Portuguese Foundation for Science and Technology FCT/MCTES (PIDDAC) through the following projects—Associate Laboratory ARISE LA/P/0112/2020; UIDP/04044/2020; UIDB/04044/2020; PAMI-ROTEIRO/0328/2013 (N° 022158); MATIS (CENTRO-01-0145-FEDER-000014-3362); DOI: 10.54499/UIDB/04044/2020; Generative. Thermodynamic; and FruitPV—and by the CDRSP and ESTG from the Polytechnic of Leiria.
dc.identifier.citationFatelo, J.P.; MartinsFerreira, N. Reconstructing Classical Algebras via Ternary Operations. Mathematics 2025, 13, 1407. https:// doi.org/10.3390/math13091407
dc.identifier.doi10.3390/math13091407
dc.identifier.issn2227-7390
dc.identifier.urihttp://hdl.handle.net/10400.8/13828
dc.language.isoeng
dc.peerreviewedyes
dc.publisherMDPI
dc.relationAdvanced Production and Intelligent Systems
dc.relationCentre for Rapid and Sustainable Product Development
dc.relation.hasversionhttps://www.mdpi.com/2227-7390/13/9/1407
dc.relation.ispartofMathematics
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectBoolean algebras
dc.subjectMV-algebras
dc.subjectde Morgan algebras
dc.subjectTernary operations
dc.subjectRings and near-rings of characteristic two
dc.titleReconstructing Classical Algebras via Ternary Operationseng
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleAdvanced Production and Intelligent Systems
oaire.awardTitleCentre for Rapid and Sustainable Product Development
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/LA%2FP%2F0112%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04044%2F2020/PT
oaire.citation.issue9
oaire.citation.titleMathematics
oaire.citation.volume13
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
person.familyNamePereira Fatelo
person.familyNameMartins-Ferreira
person.givenNameJorge
person.givenNameNelson
person.identifier485301
person.identifier.ciencia-idB115-B65E-24AA
person.identifier.orcid0000-0001-7510-5534
person.identifier.orcid0000-0002-4199-7367
person.identifier.ridN-1699-2013
person.identifier.scopus-author-id24598020700
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
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relation.isAuthorOfPublication.latestForDiscovery9396a679-0caf-42e4-be1e-31c0b37ba3ea
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