Work

On sM-Prime Ideals in Commutative Rings

Year: 2026

Type: article

Abstract: 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.

Source: Axioms

DOI: 10.3390/axioms15020142

Authors: Gülşen Ulucak, Violeta Leoreanu-Fotea, Seçil Çeken Güneş, Ünsal Tekir

Institutions: Gebze Technical University, Alexandru Ioan Cuza University, Trakya University, Marmara University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

OpenAlex ID: W7128955541

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