Generalization of ρ-ideals associated with an m-system and a special radical class

ÇAY H., Abouhalaka A., ERSOY B. A.

Ricerche di Matematica, vol.74, no.3, pp.1467-1482, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 74 Issue: 3
  • Publication Date: 2025
  • Doi Number: 10.1007/s11587-024-00912-2
  • Journal Name: Ricerche di Matematica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.1467-1482
  • Keywords: m-system, Noncommutative ring, prime ideal, S-prime ideal, Special radical classes
  • Çukurova University Affiliated: Yes

Abstract

Let ϕ≠S⊆R be an m-system of a ring R, and let ρ be a special radical. This study introduces the concept of S-ρ-ideals in noncommutative rings. This notion extends the previously studied ρ-ideals and can also be seen as a generalization of the right S-prime ideals. We show how some properties associated with ρ-ideals have evolved into results within these generalizations. Relationships between S-ρ-ideals and other types of ideals like ρ-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⊞M)-ρ-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.