On ϕ-n-absorbing primary ideals of commutative rings

Abstract

All rings are commutative with $1$ and $n$ is a positive integer. Let $\varphi :J(R)\to J(R)\cup \varnothing$ be a function where $J(R)$ denotes the set of all ideals of $R$. We say that a proper ideal $I$ of $R$ is $\varphi$-$n$-absorbing primary if whenever $a_1,a_2,...,a_{n+1}\in R$ and $a_1{a}_2\cdots a_{n+1}\in I\backslash \varphi (I)$, either $a_1{a}_2\cdots a_n\in I$ or the product of $a_{n+1}$ with $(n-1)$ of $a_1,...,a_n$ is in $\sqrt{I}$. The aim of this paper is to investigate the concept of $\varphi$-$n$-absorbing primary ideals.

29 pages