?-n-IDEALS OF COMMUTATIVE RINGS

Abstract

Let R be a commutative ring with non-zero identity, and ?: 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 ?-n-ideals which is an extension of n-ideals in commutative rings. We call a proper ideal I of R a ?-n-ideal if whenever a, b ? R with ab ? I and a /??0, then b ? ?(I). For example, an ideal expansion ?<inf>1</inf> is defined by ?<inf>1</inf> (I) =?I. In this case, a ?<inf>1</inf>-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 ?-n-ideals to characterize fields and UN-rings. © 2022 Elsevier B.V., All rights reserved.