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(2, J)-IDEALS IN COMMUTATIVE RINGS
(PUBL HOUSE BULGARIAN ACAD SCI, 2020) Yildiz, Eda; Tekir, Unsal; Koc, Suat
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.