Nil-prime ideals of a commutative ring
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916718669987840 |
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| author | Farshadifar, Faranak |
| author_facet | Farshadifar, Faranak |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19950 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nil-prime ideals of a commutative ring Farshadifar, Faranak Commutative Algebra 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. |
| title | Nil-prime ideals of a commutative ring |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2409.19950 |