Semilinear De Morgan monoids and epimorphisms
| dc.contributor.author | Wannenburg, Johann Joubert | |
| dc.contributor.author | Raftery, James G. | |
| dc.contributor.email | jamie.wannenburg@up.ac.za | en_US |
| dc.date.accessioned | 2024-01-16T05:23:50Z | |
| dc.date.available | 2024-01-16T05:23:50Z | |
| dc.date.issued | 2024-01 | |
| dc.description | DATA AVAILABILITY : Data sharing not applicable to this article as datasets were neither generated nor analysed. | en_US |
| dc.description.abstract | A 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.department | Mathematics and Applied Mathematics | en_US |
| dc.description.librarian | hj2024 | en_US |
| dc.description.sdg | None | en_US |
| dc.description.sponsorship | The 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.uri | https://link.springer.com/journal/12 | en_US |
| dc.identifier.citation | Wannenburg, 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.issn | 0002-5240 (print) | |
| dc.identifier.issn | 1420-8911 (online) | |
| dc.identifier.other | 10.1007/s00012-023-00837-1 | |
| dc.identifier.uri | http://hdl.handle.net/2263/93970 | |
| dc.language.iso | en | en_US |
| dc.publisher | Springer | en_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.subject | Epimorphism | en_US |
| dc.subject | Semilinear | en_US |
| dc.subject | Residuated lattice | en_US |
| dc.subject | De Morgan monoid | en_US |
| dc.subject | Dunn monoid | en_US |
| dc.subject | Substructural logic | en_US |
| dc.subject | Relevance logic | en_US |
| dc.subject | Beth definability | en_US |
| dc.title | Semilinear De Morgan monoids and epimorphisms | en_US |
| dc.type | Article | en_US |