{
  "abstract": "Let $π:(X,T)\\rightarrow(Y,S)$ be a factor map between zero-dimensional dynamical systems, and let $X_0$ and $Y_0$ be quasi-sections with $π(X_0)=Y_0$. We study the homomorphism $π^*:K^0(Y|Y_0,S)\\rightarrow K^0(X|X_0,T)$, $[f]\\mapsto[f\\circπ]$, between the corresponding relative dimension groups, and identify it with the homomorphism induced by the premorphism between Bratteli--Vershik realizations associated with $π$. Generalizing a result of Glasner and Weiss for minimal Cantor systems, we show that if $Y_0$ is quasi-simple, then $π^*$ is an injective unital order-preserving homomorphism, and that if $X_0=π^{-1}(Y_0)$, then $π^*$ is a unital order embedding; the latter condition is characterized in terms of the premorphism. Examples show that quasi-simplicity cannot be dropped, and that without the condition $X_0=π^{-1}(Y_0)$ the map $π^*$ need not be an order embedding.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28813",
  "author_total": 1,
  "authors": [
    {
      "name": "Maryam Hosseini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/14npr6s52dvtr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28813",
  "fulltext_url": null,
  "id": "14npr6s52dvtr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28813",
  "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.DS"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7223238538",
  "pdf_url": "https://arxiv.org/pdf/2610.28813",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/14npr6s52dvtr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.28813",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28813"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Embeddings of Relative Dimension Groups for Zero-Dimensional Dynamical Systems",
  "title_text": "Embeddings of Relative Dimension Groups for Zero-Dimensional Dynamical Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/14npr6s52dvtr",
  "venue": "arXiv",
  "versions": []
}