2-nil ideals of commutative rings

Abstract

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. © 2021 Belgian Mathematical Society. All rights reserved.