GENERALIZATIONS OF RADICAL IDEALS IN NONCOMMUTATIVE RINGS

Document Type : Original Manuscript

Author

Department of Mathematics, Nelson Mandela University, Gqeberha, South Africa.

10.22044/jas.2024.12957.1709

Abstract

In this study, we present the generalization of the concept of radical-ideals in noncommutative rings with nonzero identity. Let R be a noncommutative ring with 1≠0 and S(R) be the set of all ideals of R. Let φ : S(R) →S(R)∪∅ be a function and let ρ be a special radical. A proper ideal I of R is said to be a φ -ρ ideal of R if whenever a,b∈R with aRb⊆I and aRb⊈φ(I) and a∉ρ(R) then b∈I. Many of the results on n-ideals, J-ideals and there generalizations like weakly n-ideals and weakly J-ideals will follow as special cases from results proved for φ -ρ ideals in this paper.

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References

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Journal of Algebraic Systems
Volume 14, Issue 1
January 2026
Pages 93-112

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