(2, J)-IDEALS IN COMMUTATIVE RINGS


YILDIZ E. , TEKİR Ü., KOÇ S.

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, vol.73, no.9, pp.1201-1209, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 73 Issue: 9
  • Publication Date: 2020
  • Doi Number: 10.7546/crabs.2020.09.02
  • Title of Journal : COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES
  • Page Numbers: pp.1201-1209

Abstract

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.