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- Title
On ϕ-(n,N)-ideals of Commutative Rings.
- Authors
Anebri, Adam; Mahdou, Najib; Tekir, Ünsal; Yıldız, Eda
- Abstract
Let R be a commutative ring with nonzero identity and n be a positive integer. In this paper, we introduce and investigate a new subclass of ϕ - n -absorbing primary ideals, which are called ϕ - (n , N) -ideals. Let ϕ : I (R) → I (R) ∪ { ∅ } be a function, where I (R) denotes the set of all ideals of R. A proper ideal I of R is called a ϕ - (n , N) -ideal if x 1 ⋯ x n + 1 ∈ I \ ϕ (R) and x 1 ⋯ x n ∉ I imply that the product of x n + 1 with (n − 1) of x 1 , ... , x n is in 0 for all x 1 , ... , x n + 1 ∈ R. In addition to giving many properties of ϕ - (n , N) -ideals, we also use the concept of ϕ - (n , N) -ideals to characterize rings that have only finitely many minimal prime ideals.
- Subjects
PRIME ideals; COMMUTATIVE rings; INTEGERS
- Publication
Algebra Colloquium, 2023, Vol 30, Issue 3, p481
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386723000391