On ϕ-( n,N )-ideals of Commutative Rings

作     者：Adam Anebri Najib Mahdou Ünsal Tekir Eda Yıldız Adam Anebri;Najib Mahdou;Ünsal Tekir;Eda Yildiz

作者机构：Laboratory of Modelling and Mathematical StructuresDepartment of MathematicsFaculty of Science and Technology of FezBox 2202University S.M.Ben Abdellah FezMorocco Department of MathematicsMarmara UniversityIstanbulTurkey Department of MathematicsYildiz Technical University34220IstanbulTurkey 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2023年第30卷第3期

页      面：481-492页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Φ-(n N)-ideal Φ-n-absorbing primary ideal Φ-n-absorbing ideal Φ-prime 

摘      要：Let R be a commutative ring with nonzero identity and n be a positive *** this paper,we introduce and investigate a new subclass ofϕ-n-absorbing primary ideals,which are calledϕ-(n,N)-***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 aϕ-(n,N)-ideal if x1⋯xn+1∈I\ϕ(R)and x1⋯xn∉I imply that the product of xn+1 with(n−1)of x1,…,xn is in 0–√for all x1,…,xn+1∈*** addition to giving many properties ofϕ-(n,N)-ideals,we also use the concept ofϕ-(n,N)-ideals to characterize rings that have only finitely many minimal prime ideals.