On weakly s-ρ-ideals in noncommutative rings - Abouhalaka, Alaa; Çay, Hatice; Groenewald, Nico (My University, 2024)
Let 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].
Keywords: And Phrases; Weakly S-Ρ-Ideal; M-System; Noncommutative Ring; S-Ρ-Ideal; Special Radical Classes