Publicação
A note on varieties of ordered algebras
| datacite.subject.sdg | 04:Educação de Qualidade | |
| datacite.subject.sdg | 09:Indústria, Inovação e Infraestruturas | |
| datacite.subject.sdg | 17:Parcerias para a Implementação dos Objetivos | |
| dc.contributor.author | Clementino, Maria Manuel | |
| dc.contributor.author | Rodelo, Diana | |
| dc.date.accessioned | 2026-09-02T13:00:48Z | |
| dc.date.available | 2026-09-02T13:00:48Z | |
| dc.date.issued | 2026-11 | |
| dc.description.abstract | The aim of this work is to study the notions of lax protomodular and Ord-Mal’tsev category at the level of (coherent) varieties of (pre)ordered algebras and to further compare them, as has been done in the non-ordered context. We characterise varieties of ordered algebras which are (co)lax protomodular and those which are Ord-Mal’tsev, in terms of operations of arities given by ordered sets and inequalities involving them. We exhibit examples of (co)lax protomodular non-degenerate Ordcategories, which were unknown. We prove that, for varieties of ordered algebras which are Ord-Mal’tsev categories, the order of their algebras is degenerate (i.e. is symmetric). As a consequence, the implication ``protomodular ⇒ Mal’tsev'' cannot be carried out to our context. The case of non-coherent ordered varieties which are Ord-Mal’tsev categories is also addressed, where we show the existence of algebras with non-degenerate order. | eng |
| dc.identifier.doi | 10.1016/j.jpaa.2026.108363 | |
| dc.identifier.issn | 0022-4049 | |
| dc.identifier.uri | http://hdl.handle.net/10400.1/29387 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Elsevier BV | |
| dc.relation.ispartof | Journal of Pure and Applied Algebra | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | Categories enriched in the category of preorders | |
| dc.subject | Mal’tsev categories. Varieties of ordered algebras | |
| dc.subject | Mal’tsev operation | |
| dc.title | A note on varieties of ordered algebras | eng |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.issue | 11 | |
| oaire.citation.startPage | 108363 | |
| oaire.citation.title | Journal of Pure and Applied Algebra | |
| oaire.citation.volume | 230 | |
| oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |
| person.familyName | Rodelo | |
| person.givenName | Diana | |
| person.identifier.ciencia-id | 6C16-FCF9-64A0 | |
| person.identifier.orcid | 0000-0002-4816-3234 | |
| person.identifier.rid | AFH-8267-2022 | |
| person.identifier.scopus-author-id | 8216708900 | |
| relation.isAuthorOfPublication | 311bbe08-1f8a-4c84-87e7-23ddd55c89a3 | |
| relation.isAuthorOfPublication.latestForDiscovery | 311bbe08-1f8a-4c84-87e7-23ddd55c89a3 |