On quasi-(2,n)-ideals of commutative rings

Abstract

Let A be a commutative ring with nonzero identity and I a proper ideal of A. I is said to be a quasi-(2,n)-ideal if whenever root I is a (2,n)-ideal of A. In this paper, we aim to give the relations between quasi-(2,n)-ideals and other classical ideals such as (2,n)-ideals, n-ideals and 2-absorbing quasi-primary ideals. In addition to give many properties, characterizations and examples of this new class of ideals, we also characterize some important class of rings such as UN-rings, reduced rings with at most two minimal prime ideals, integral domains, direct product of two integral domains in terms of quasi-(2,n)-ideals.