Generalizations of almost prime and right S-prime ideals in noncommutative rings

Abouhalaka A., Groenewald N., FINDIK Ş.

Sao Paulo Journal of Mathematical Sciences, cilt.19, sa.2, 2025 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s40863-025-00512-4
  • Dergi Adı: Sao Paulo Journal of Mathematical Sciences
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Anahtar Kelimeler: Almost prime ideals, Almost S-prime ideals, Noncommutative rings, Prime ideals, S-prime ideals
  • Çukurova Üniversitesi Adresli: Evet

Özet

Let R be a noncommutative ring, and let S be an m-system of R. In this paper, we give more results on the concept of almost prime (right) ideals, that were introduced in Abouhalaka and Fındık (Serdica Math J 48:235–246, 2022), particularly, in (right) S-unital rings, local rings, and decomposable rings. In addition, we introduce the concept of almost right S-prime ideals, and we show how some findings regarding almost prime ideals can be derived as corollaries of almost right S-prime ideals. Additionally, we show how almost right S-prime ideals behave in related rings such as homomorphic images, quotient rings, and decomposable rings. Finally, we construct almost right S-prime ideals using the Nagata method of Idealization.