2J-ideals in commutative rings

The notion of 2J-ideals in commutative rings is presented in this article. The symbols N(A) and J(A) stand for A’s nil-radical and Jacobson radicals, respectively. In this paper, we present and investigate a new Extension of J-ideals named 2J-ideals. A proper ideal I1 of a ring A is named a 2J-ideal if every time a, b ∈ A with a, b ∈ I1 and a ∉ J(A), then b2 ∈ I1. We investigate the relationships between this class of ideals and several other classes of ideals, as well as many of its characteristics and instances.