{
  "abstract": "Let $0 \\xrightarrow{}I \\xrightarrow{ } A \\xrightarrow{ }A/I \\xrightarrow{} 0$ be a short exact sequence of C*-algebras. In this paper, we prove that if $\\dim({\\rm Cu}(I))\\leq n$ and $\\dim({\\rm Cu}(A/I))\\leq m$, then $\\dim({\\rm Cu}(A))\\leq n+m+1$, this result gives an affirmative answer to a problem concerning the Cu-semigroup of C*-algebras raised by Thiel and Vilalta. We further show that certain comparison and divisibility properties satisfied by $I$ and $A/I$ are inherited by the extension algebra $A$. As an application, we provide an alternative proof of equivalence that $A$ is pure if and only if $I$ and $A/I$, a result originally proven by Perera, Thiel, and Vilalta.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27694",
  "author_total": 1,
  "authors": [
    {
      "name": "Qingzhai Fan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/96a1vjsfdk7kb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27694",
  "fulltext_url": null,
  "id": "96a1vjsfdk7kb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27694",
  "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.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214162124",
  "pdf_url": "https://arxiv.org/pdf/2609.27694",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/96a1vjsfdk7kb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27694",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27694"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Certain Cuntz semigroup properties of extension C*-algebras",
  "title_text": "Certain Cuntz semigroup properties of extension C*-algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/96a1vjsfdk7kb",
  "venue": "arXiv",
  "versions": []
}