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Peer-reviewedCC BY 4.0Mathematics

On PS-Injective Modules

  • Ergül Türkmen1
  • Engin Kaynar2
  • Yıldız Aydın3
  1. 1Department of Mathematics, Faculty of Humanities and Social Sciences, Amasya University, 05100 Amasya, Türkiye
  2. 2Vocational School of Technical Sciences, Amasya University, 05100 Amasya, Türkiye
  3. 3Department of Management and Information Systems, Istanbul Gelişim University, 34310 Istanbul, Türkiye
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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.

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Cite

BibTeXRIS
BibTeX
@article{turkmen2026psinjective,
  title = {{On PS-Injective Modules}},
  author = {Ergül Türkmen and Engin Kaynar and Yıldız Aydın},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203785},
  url = {https://www.mdpi.com/2227-7390/14/20/3785},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - On PS-Injective Modules
AU  - Ergül Türkmen
AU  - Engin Kaynar
AU  - Yıldız Aydın
PY  - 2026
DA  - 2026/10/18
JO  - Mathematics
DO  - 10.3390/math14203785
UR  - https://www.mdpi.com/2227-7390/14/20/3785
AB  - 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.
SN  - 2227-7390
ER  -