Yazar "Abouhalaka, Alaa" seçeneğine göre listele

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    Generalization of ρ-ideals associated with an m-system and a special radical class
    (2025) Çay, Hatice; Abouhalaka, Alaa; Ersoy, Bayram Ali
    Let phi not equal S subset of R be an m-system of a ring R, and let. be a special radical. This study introduces the concept of S-rho-ideals in noncommutative rings. This notion extends the previously studied rho-ideals and can also be seen as a generalization of the right S-prime ideals. We show how some properties associated with rho-ideals have evolved into results within these generalizations. Relationships between S-rho-ideals and other types of ideals like rho-ideals, right S-prime ideals, and S-finite ideals are shown. We show the behaviour of this notion in related rings. The construction of (S boxed plus M)-rho-ideals in idealization rings is presented for an R- R-bimodule M. Additionally, we introduce S-P-ideals using Baer-McCoy radical P and examine their properties.
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    On weakly s-ρ-ideals in noncommutative rings
    (2024) Abouhalaka, Alaa; Çay, Hatice; Groenewald, Nico
    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].
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    S-j-ideals: a study in commutative and noncommutative rings
    (2024) Abouhalaka, Alaa; Çay, Hatice; Ersoy, Bayram Ali
    In this paper, we introduce the concept of S- (Formula presented.) -ideals in both commutative and noncommutative rings. For a commutative ring R and a multiplicatively closed subset S, we show that many properties of (Formula presented.) -ideals apply to S- (Formula presented.) -ideals and examine their characteristics in various ring constructions, such as homomorphic image rings, quotient rings, cartesian product rings, polynomial rings, power series rings, idealization rings, and amalgamation rings. In noncommutative rings, where S is an m-system, we define right S- (Formula presented.) -ideals. We demonstrate the equivalence of S- (Formula presented.) -ideals and right S- (Formula presented.) -ideals in commutative rings with identity and provide examples to illustrate the connections between right S-prime ideals and (Formula presented.) -ideals.