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Open Access Research Article

On e-primary ideals of commutative rings

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pp. 2005–2011Vol. 29Issue 5May 2026DOI: 10.47974/JDMSC-2382 Crossmark XML
Received:
01 May 2025
Published Online:
22 May 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2382
Pages:
2005–2011

Abstract

This work studies a novel generalization of primary ideals called ᶒ-primary ideals in commutative rings. We aim to investigate properties of primary ideals that extend naturally to ᶒ-primary ideals. If п is the proper ideals for the commutative rings with unity H, and ᶒ ∈ H an idempotent element such that ᶒ ∉ п. The ideals п is named ᶒ-primary ideals in the rings H if for h, k ∈ H with hk ∈ п, we have that ᶒh ∈ п or ᶒk ∈ rad(п). We settle and generalize multiple results from primary ideals to ᶒ-primary ideals. Furthermore, we study certain characterizations of ᶒ-primary ideals in the idealizations for the module H(+)M and amalgamations duplications for ring H ⋈Ψ z.

Keywords

Subject Classifications

13A1513C05

References

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