{
  "abstract": "Let $S$ be a minimally four-generated numerical semigroup that is nearly Gorenstein but not almost symmetric, and let $R=\\Bbbk[S]$ over an arbitrary field $\\Bbbk$. We prove that the defining ideal of $R$ has four or five minimal generators when $R$ has Cohen--Macaulay type two, and exactly six when it has type three. Thus the total Betti sequence over the four-variable polynomial presentation ring is one of\n\n$$\n\n(1,4,5,2),\\quad (1,5,6,2),\\quad (1,6,8,3),\n\n$$\n\nand all three possibilities occur. The type-three argument uses a canonical-ideal exact sequence, a chain-level comparison on Tor, and a codimension-three Gorenstein reduction. The resulting classification gives an affirmative answer, over every field, to Moscariello and Strazzanti's Question~4.3 on four-generated nearly Gorenstein numerical semigroups that are not almost symmetric.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Zhi-Lin Zhang",
      "orcid": "0009-0000-5206-3538"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/92z64a091pfxv.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23538799",
  "fulltext_url": null,
  "id": "92z64a091pfxv",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23538799",
  "language": "eng",
  "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": null,
  "pdf_url": "https://zenodo.org/api/records/23538799/files/v3.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/92z64a091pfxv.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:21:01Z",
      "native_id": "23538799",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23538799"
    }
  ],
  "subjects": [],
  "title": "Betti sequences of four-generated non-almost-symmetric nearly Gorenstein numerical semigroup rings",
  "title_text": "Betti sequences of four-generated non-almost-symmetric nearly Gorenstein numerical semigroup rings",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:01Z",
  "url": "https://research.draconitic.com/paper/92z64a091pfxv",
  "venue": "Zenodo",
  "versions": []
}