{
  "abstract": "Let $\\Rn$ be the variety of rings satisfying $x^n\\eqid x$, where $n\\geq2$, and let $\\W$ be a variety of idempotent semirings with commutative addition. The equality $\\Rn\\circ\\W=\\Rn\\vee\\W$ holds, and this variety has subvariety lattice $L(\\Rn)\\times L(\\W)$. Its subdirectly irreducible members that are not additively idempotent have exactly one nontrivial ring component, which is a finite field. Such a member is determined by this field and an idempotent semiring with a multiplicative identity; a separation condition on unary polynomial functions of the latter characterizes subdirect irreducibility. Every subvariety has a finite identity basis. A four-element semiring generates a variety with subdirectly irreducible members of unbounded cardinality. The results extend the Mal'cev product theorem of Wang and Shao from the absorption subvariety to arbitrary $\\W\\leq\\Slp$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12188",
  "author_total": 2,
  "authors": [
    {
      "name": "Aifa Wang"
    },
    {
      "name": "Lili Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ctq3q3dm3fjca.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12188",
  "fulltext_url": null,
  "id": "ctq3q3dm3fjca",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12188",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7221117482",
  "pdf_url": "https://arxiv.org/pdf/2610.12188",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ctq3q3dm3fjca.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12188",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12188"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Mal'cev products of rings satisfying $x^n\\approx x$ and idempotent semirings",
  "title_text": "Mal'cev products of rings satisfying x^n≈ x and idempotent semirings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/ctq3q3dm3fjca",
  "venue": "arXiv",
  "versions": []
}