{
  "abstract": "In this paper, we introduce the concept of ps-injective modules, which plays a key role in our approach. We develop the various properties of these modules. In particular, we prove that for a ring R, every projective semisimple R-module is injective if and only if every R-module is ps-injective. Furthermore, we show that every ps-injective R-module is injective if and only if R is a left semiartinian and left SI-ring. In addition, using the projective socle of the ring R, we investigate in detail the structure of modules whose socle is singular.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Faculty of Humanities and Social Sciences, Amasya University, 05100 Amasya, Türkiye",
    "Vocational School of Technical Sciences, Amasya University, 05100 Amasya, Türkiye",
    "Department of Management and Information Systems, Istanbul Gelişim University, 34310 Istanbul, Türkiye"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ergül Türkmen",
      "orcid": "0000-0002-7082-1176"
    },
    {
      "affs": [
        1
      ],
      "name": "Engin Kaynar",
      "orcid": "0000-0002-1955-1326"
    },
    {
      "affs": [
        2
      ],
      "name": "Yıldız Aydın",
      "orcid": "0000-0001-9061-0109"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cnrxvepcnzdzj.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203785",
  "fulltext_url": null,
  "id": "cnrxvepcnzdzj",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3785",
  "language": null,
  "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",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7222967724",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/cnrxvepcnzdzj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203785",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3785"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Rings, Modules, and Algebras",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On PS-Injective Modules",
  "title_text": "On PS-Injective Modules",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/cnrxvepcnzdzj",
  "venue": "Mathematics",
  "versions": []
}