{
  "abstract": "For an Artin algebra $Λ$, we define the class of locally Gorenstein modules, which is a generalization of semi-Gorenstein projective modules and, therefore, a generalization of projective Gorenstein modules. For a locally Gorenstein module $X\\in{\\rm mod}\\ Λ$ we construct $\\underline{χ}_X$ a subcategory of $\\underline{\\rm mod}$ $Λ$ and we prove that the syzygy functor is faithful and full on $\\underline{χ}_X$. Using that, we prove that the Igusa-Todorov functions $ϕ$ and $ψ$ vanish on the family of locally Gorenstein modules. Finally, using locally Gorenstein modules, we define the locally Gorenstein algebras, a generalization of Gorenstein algebras, and we prove that their finitistic, and the $ϕ$ and $ψ$ dimensions are finite.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23592",
  "author_total": 3,
  "authors": [
    {
      "name": "Leonardo Alarcon"
    },
    {
      "name": "María Andrea Gatica"
    },
    {
      "name": "Marcelo Lanzilotta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9c2cs3g5qh42k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23592",
  "fulltext_url": null,
  "id": "9c2cs3g5qh42k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23592",
  "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.AC"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7222986799",
  "pdf_url": "https://arxiv.org/pdf/2610.23592",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9c2cs3g5qh42k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23592",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23592"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Locally Gorenstein algebras, a generalization of Gorenstein algebras",
  "title_text": "Locally Gorenstein algebras, a generalization of Gorenstein algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/9c2cs3g5qh42k",
  "venue": "arXiv",
  "versions": []
}