Generalization of ρ-ideals associated with an m-system and a special radical class - Cay, Hatice; Abouhalaka, Alaa; Ersoy, Bayram Ali (SPRINGER-VERLAG ITALIA SRL, 2025)
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.
Keywords: prime ideal; S-prime ideal; m-system; Special radical classes; Noncommutative ring; N-IDEALS; RINGS; Mathematics