(2, J)-IDEALS IN COMMUTATIVE RINGS


Yıldız E. , Tekir Ü., Koç S.

Comptes Rendus De L Academie Bulgare Des Sciences, cilt.73, ss.1201-1209, 2020 (SCI Expanded İndekslerine Giren Dergi)

  • Cilt numarası: 73 Konu: 9
  • Basım Tarihi: 2020
  • Doi Numarası: 10.7546/crabs.2020.09.02
  • Dergi Adı: Comptes Rendus De L Academie Bulgare Des Sciences
  • Sayfa Sayıları: ss.1201-1209

Özet

Let A be a commutative ring with nonzero identity. In this paper, we introduce the concept of (2, J)-ideal as a generalization of J-ideal. A proper ideal P of A is said to be a (2, J)-ideal if whenever abc ∈ P and a, b, c ∈ A, then ab ∈ P or ac ∈ Jac(A) or bc ∈ Jac(A). Various examples and characterizations of (2, J)-ideals are given. Also, we study many properties of (2, J)-ideals and use them to characterize certain classes of rings such as quasi-local rings and Artinian rings.