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:J(R)→ J(R)U {Ø} be a function,where J(R)denotes the set of all ideals of R.A proper ideal I of R is called a φ-(n,N)-ideal if x1 … xn+1 ∈ I\φ(I)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 ∈ R.In addition to giving many properties ofφ-(n,N)-ideals,we also use the concept of φ-(n,N)-ideals to characterize rings that have only finitely many minimal prime ideals.
Laboratory of Modelling and Mathematical Structures Department of Mathematics,Faculty of Science and Technology of Fez Box 2202,University S.M.Ben Abdellah Fez,Morocco
Department of Mathematics,Marmara University,Istanbul,Turkey
Department of Mathematics,Yildiz Technical University,34220,Istanbul,Turkey
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