Nil-primary ideals of a commutative ring

چکیده مقاله

Let R be a commutative ring with identity and Nil(R) be the set of all nilpotent elements of R. In this paper, we introduce the notion of nil-primary ideals as a generalization of primary ideals and we investigate some nil-versions of the well-known results about primary ideals. We say that a proper ideal P of R is a nil-primary ideal if there exists x∈Nil(R) such that whenever ab∈P for some a,b∈R, then a∈P or bn∈P or a+x∈P or bn+x∈P for some n∈N. © The Author(s) under exclusive license to Università degli Studi di Ferrara 2026.