{
  "abstract": "Nodal filters provide an order-theoretic approach to the study of the filter structure of algebraic systems. In this paper, we investigate nodal filters in equality algebras, with particular emphasis on nodal filters of types 1, 2, and 3. We first establish several structural properties of these filters and examine their relationships with positive implicative and implicative filters. In particular, we show that, under suitable conditions, such as purity and density, important classes of filters are nodal. We also provide examples and counterexamples to illustrate the scope and limitations of these results. We then introduce operations on the set of all nodal filters of type 1 and study the resulting algebraic structure. We prove that this structure forms an L-algebra and a bounded distributive lattice. Furthermore, by defining a suitable operation, we show that it is a residuated lattice, an MTL-algebra and a BL-algebra. We also establish that the resulting structure is a semi-De Morgan algebra, a bounded equality algebra, and a Stonean equality algebra. Finally, several additional algebraic identities and order-theoretic properties are obtained, providing further insight into the interaction between nodal filters and the algebraic structure induced by their operations.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Tarbiat Modares University, Tehran 14115-134, Iran",
    "Department of Mathematics, Graduate University of Advanced Technology, Kerman 76311-33131, Iran",
    "Center for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Hamid Reza Asadi Dehaghi",
      "orcid": "0009-0007-2895-9175"
    },
    {
      "affs": [
        1
      ],
      "name": "Mohammad Mahdi Zahedi",
      "orcid": "0000-0003-3197-9904"
    },
    {
      "affs": [
        2
      ],
      "name": "Hashem Bordbar",
      "orcid": "0000-0003-3871-217X"
    },
    {
      "affs": [
        0
      ],
      "name": "Ali Iranmanesh",
      "orcid": "0000-0003-2639-9454"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c3ypp60d2qqdq.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15100766",
  "fulltext_url": null,
  "id": "c3ypp60d2qqdq",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/10/766",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7204038941",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/c3ypp60d2qqdq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:30Z",
      "native_id": "10.3390/axioms15100766",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/10/766"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "journal-openalex:F26",
      "subfield": "general"
    }
  ],
  "title": "Nodal Filters in Equality Algebras",
  "title_text": "Nodal Filters in Equality Algebras",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:30Z",
  "url": "https://research.draconitic.com/paper/c3ypp60d2qqdq",
  "venue": "Axioms",
  "versions": []
}