δ-n-IDEALS OF COMMUTATIVE RINGS

Abstract

Let R be a commutative ring with non-zero identity, and δ: I(R) → I(R) be an ideal expansion where I(R) is the set of all ideals of R. In this paper, we introduce the concept of δ-n-ideals which is an extension of n-ideals in commutative rings. We call a proper ideal I of R a δ-n-ideal if whenever a, b ∈ R with ab ∈ I and a /∈√0, then b ∈ δ(I). For example, an ideal expansion δ1 is defined by δ1 (I) =√I. In this case, a δ1-n-ideal I is said to be a quasi n-ideal or equivalently, I is quasi n-ideal if √ I is an n-ideal. A number of characterizations and results with many supporting examples concerning this new class of ideals are given. In particular, we present some results regarding quasi n-ideals. Furthermore, we use δ-n-ideals to characterize fields and UN-rings. © 2022, University of Guilan. All rights reserved.