Abouhalaka, AlaaÇay, HaticeGroenewald, Nico2025-12-092025-12-092024Abouhalaka, A., Çay, H. ve Groenewald, N. (2024). On weakly s-ρ-ideals in noncommutative rings. Gulf Journal of Mathematics, 18(2), 1-15. http://dx.doi.org/10.56947/gjom.v18i2.22212309-4966http://dx.doi.org/10.56947/gjom.v18i2.2221https://hdl.handle.net/20.500.12511/13310Let R be a noncommutative ring, and φ ≠ S ⊆ R be an m-system of R. In this paper, we extend the concept of weakly prime ideals in noncommutative rings by introducing weakly S-ρ-ideals. This generalization builds on the notions of right S-prime, weakly S-n-ideals and S-ρ-ideals. We present equivalent definitions and key properties of weakly S-ρ-ideals. We also explore with the method of idealization how the weakly S-ρ-ideal property transfers to related rings and construct such ideals. On the other hand we give a generalization of S-J-ideals which were introduced in [12].eninfo:eu-repo/semantics/openAccessAnd PhrasesWeakly S-Ρ-IdealM-SystemNoncommutative RingS-Ρ-IdealSpecial Radical ClassesArticle18211510.56947/gjom.v18i2.22212-s2.0-85212195435Q3