ON WEAKLY S-ρ-IDEALS IN NONCOMMUTATIVE RINGS

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Abouhalaka A., ÇAY H., Groenewald N.

Gulf Journal of Mathematics, vol.18, no.2, pp.1-15, 2024 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.56947/gjom.v18i2.2221
  • Journal Name: Gulf Journal of Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.1-15
  • Keywords: and phrases. weakly S-ρ-ideal, m-system, noncommutative ring, S-ρ-ideal, special radical classes
  • Çukurova University Affiliated: Yes

Abstract

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].