{
  "abstract": "In this paper, we study various aspects of perspectivity in modules. We prove that the following classes of modules satisfy the perspective-Schröder-Bernstein property: modules with transitive perspectivity, quasi-continuous modules, Harada (and hence discrete) modules and quasi-discrete modules with the (finite) exchange property. Furthermore, we prove that for a semiregular ring, the Schröder-Bernstein property implies the perspective-Schröder-Bernstein property. We prove that for $A,B \\subseteq ^{\\oplus} M$, if all complements of $A$ are perspective with $B$, then all complements of $B$ are perspective with $A$. We also provide new characterizations of weakly perspective modules and modules in which perspectivity is transitive. Some applications of these results are given. We finally prove that perspectivity is transitive in a ring $R$ if and only if every special clean element of $R$ is perspective.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39491",
  "author_total": 2,
  "authors": [
    {
      "name": "Dinesh Khurana"
    },
    {
      "name": "Shubham Mittal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cj6e8e14g3n24.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39491",
  "fulltext_url": null,
  "id": "cj6e8e14g3n24",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39491",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7215038217",
  "pdf_url": "https://arxiv.org/pdf/2609.39491",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cj6e8e14g3n24.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39491",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39491"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Perspectivity and the perspective-Schröder-Bernstein Property",
  "title_text": "Perspectivity and the perspective-Schröder-Bernstein Property",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/cj6e8e14g3n24",
  "venue": "arXiv",
  "versions": []
}