The concept of 2-nil ideal of a commutative ring R is introduced, as an alternative to the $(2,n)$-ideals from [6]. We study its relationship with previously introduced classes of ideals, such as 2-absorbing ideals and n-ideals. Various properties and examples are presented. Our main result is a characterization of rings for which every 2-nil ideal is prime. We give a description of 2-nil ideals of general ZPI-rings.
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Ece Yetki̇n Çeli̇kel (2021) studied this question.