On sM-Prime Ideals in Commutative Rings

Ulucak, Gülşen; Leoreanu-Fotea, Violeta; Çeken Güneş, Seçil; Tekir, ÜNSAL

doi:10.3390/axioms15020142

On sM-Prime Ideals in Commutative Rings

Ulucak G., Leoreanu-Fotea V., Çeken Güneş S., Tekir Ü.

Axioms, cilt.15, sa.2, ss.1-13, 2026 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 15 Sayı: 2
Basım Tarihi: 2026
Doi Numarası: 10.3390/axioms15020142
Dergi Adı: Axioms
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), zbMATH, Directory of Open Access Journals
Sayfa Sayıları: ss.1-13
Marmara Üniversitesi Adresli: Evet

Özet

All rings considered are commutative with identity, and all modules are assumed to be unital. In this paper, we study R-modules in which every quasi-primary submodule is also primary; we refer to such modules as satisfying condition (*). We present several structural properties of these modules and investigate when the direct sum of two modules $𝑀 1$ and $𝑀 2$ inherits condition (*). In addition, we focus on prime ideals P of a ring R with the property that any P-quasi-primary submodule of an R-module M is automatically P-primary. Prime ideals exhibiting this behaviour are introduced as weak $𝑠 𝑀$ -prime ideals relative to M. Our results provide a framework for understanding the interaction between the quasi-primary structure of modules and the prime spectrum of the underlying ring.