Nil-prime ideals of a commutative ring
Abstract
Let R be a commutative ring with identity and N(R) be the set of all nilpotent elements of R. The aim of this paper is to introduce and study the notion of nil-prime ideals as a generalization of prime ideals. We say that a proper ideal P of R is a nil-prime ideal if there exists x \in N(R) and whenever ab \in P, then a \in P or b \in P or a+x \in P or b+x \in P for each a,b \in R. Also, we introduce nil versions of some algebraic concepts in ring theory such as nil-maximal ideal, nil-minimal ideal, nil-principal ideal and investigate some nil-version of a well-known results about them.
Fields of Study & Subjects
Rings
Modules
and Algebras
Advanced Topics in Algebra
Advanced Algebra and Logic
Publication details
- Journal / source
- Communications in Algebra
- Publisher
- Informa UK Limited
- Pages
- 1–7
- Publication date
- 2 September 2026
- Language
- EN