Semilinear De Morgan monoids and epimorphisms

dc.contributor.authorWannenburg, Johann Joubert
dc.contributor.authorRaftery, James G.
dc.contributor.emailjamie.wannenburg@up.ac.zaen_US
dc.date.accessioned2024-01-16T05:23:50Z
dc.date.available2024-01-16T05:23:50Z
dc.date.issued2024-01
dc.descriptionDATA AVAILABILITY : Data sharing not applicable to this article as datasets were neither generated nor analysed.en_US
dc.description.abstractA representation theorem is proved for De Morgan monoids that are (i) semilinear, i.e., subdirect products of totally ordered algebras, and (ii) negatively generated, i.e., generated by lower bounds of the neutral element. Using this theorem, we prove that the De Morgan monoids satisfying (i) and (ii) form a variety—in fact, a locally finite variety. We then prove that epimorphisms are surjective in every variety of negatively generated semilinear De Morgan monoids. In the process, epimorphism-surjectivity is established for several other classes as well, including the variety of all semilinear idempotent commutative residuated lattices and all varieties of negatively generated semilinear Dunn monoids. The results settle natural questions about Beth-style definability for a range of substructural logics.en_US
dc.description.departmentMathematics and Applied Mathematicsen_US
dc.description.librarianhj2024en_US
dc.description.sdgNoneen_US
dc.description.sponsorshipThe Operational Programme Research, Development and Education of the Ministry of Education, Youth and Sports of the Czech Republic, the EU and in part by the National Research Foundation of South Africa. Open access funding provided by University of Pretoria.en_US
dc.description.urihttps://link.springer.com/journal/12en_US
dc.identifier.citationWannenburg, J.J., Raftery, J.G. Semilinear De Morgan monoids and epimorphisms. Algebra universalis 85, 10 (2024). https://doi.org/10.1007/s00012-023-00837-1.en_US
dc.identifier.issn0002-5240 (print)
dc.identifier.issn1420-8911 (online)
dc.identifier.other10.1007/s00012-023-00837-1
dc.identifier.urihttp://hdl.handle.net/2263/93970
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.rights© 2024 The Author(s). Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License.en_US
dc.subjectEpimorphismen_US
dc.subjectSemilinearen_US
dc.subjectResiduated latticeen_US
dc.subjectDe Morgan monoiden_US
dc.subjectDunn monoiden_US
dc.subjectSubstructural logicen_US
dc.subjectRelevance logicen_US
dc.subjectBeth definabilityen_US
dc.titleSemilinear De Morgan monoids and epimorphismsen_US
dc.typeArticleen_US

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