(2, J)-IDEALS IN COMMUTATIVE RINGS

YILDIZ E., TEKİR Ü., KOÇ S.

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, cilt.73, sa.9, ss.1201-1209, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 73 Sayı: 9
  • Basım Tarihi: 2020
  • Doi Numarası: 10.7546/crabs.2020.09.02
  • Dergi Adı: COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, zbMATH
  • Sayfa Sayıları: ss.1201-1209
  • Yıldız Teknik Üniversitesi Adresli: Evet

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 is an element of P and a, b, c is an element of A, then ab is an element of P or ac is an element of Jac(A) or be is an element of 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.