On PS-Injective Modules
Year: 2026
Type: article
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.
Source: Mathematics
DOI: 10.3390/math14203785
Authors: Ergül Türkmen, Engin Kaynar, Yıldız Aydın
Institutions: Amasya Üniversitesi, İstanbul Gelişim Üniversitesi
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7222967724