Ulucak G., Leoreanu-Fotea V., Çeken Güneş S., Tekir Ü.
Axioms, cilt.15, sa.2, ss.1-13, 2026 (SCI-Expanded)
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Yayın Türü:
Makale / Tam Makale
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Cilt numarası:
15
Sayı:
2
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Basım Tarihi:
2026
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Doi Numarası:
10.3390/axioms15020142
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Dergi Adı:
Axioms
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Derginin Tarandığı İndeksler:
Science Citation Index Expanded (SCI-EXPANDED), zbMATH, Directory of Open Access Journals
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Sayfa Sayıları:
ss.1-13
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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 𝑀1 and 𝑀2 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 𝑠𝑀-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.