{
  "abstract": "This paper is the fourth in a series devoted to the finite basis problem for $4$-element additively idempotent semirings. These algebras are divided into five types according to their additive reducts; we study the largest of these types, namely those whose additive reducts are chains. Up to isomorphism, there are $386$ such algebras, denoted by $S_{(4, k)}$, $481 \\leq k \\leq 866$. We show that all but three of them, namely $S_{(4,545)}$, $S_{(4,634)}$, and $S_{(4,710)}$, are finitely based. This completes the classification, with respect to the finite basis property, of all $4$-element additively idempotent semirings with chain additive reducts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32152",
  "author_total": 6,
  "authors": [
    {
      "name": "Miaomiao Ren"
    },
    {
      "name": "Mengya Yue"
    },
    {
      "name": "Mengyu Yuan"
    },
    {
      "name": "Simin Lyu"
    },
    {
      "name": "Chenyu Yang"
    },
    {
      "name": "Ting Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ab0q86ag7v70z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32152",
  "fulltext_url": null,
  "id": "ab0q86ag7v70z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32152",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7214795959",
  "pdf_url": "https://arxiv.org/pdf/2609.32152",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ab0q86ag7v70z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32152",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32152"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The finite basis problem for additively idempotent semirings of order four, IV",
  "title_text": "The finite basis problem for additively idempotent semirings of order four, IV",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/ab0q86ag7v70z",
  "venue": "arXiv",
  "versions": []
}