# ON 𝜙-n-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS

• Mostafanasab, Hojjat ;
• Published : 2016.05.01
• 50 9

#### Abstract

All rings are commutative with $1{\neq}0$ and n is a positive integer. Let ${\phi}:{\Im}(R){\rightarrow}{\Im}(R){\cup}\{{\emptyset}\}$ be a function where ${\Im}(R)$ denotes the set of all ideals of R. We say that a proper ideal I of R is ${\phi}$-n-absorbing primary if whenever $a_1,a_2,{\cdots},a_{n+1}{\in}R$ and $a_1,a_2,{\cdots},a_{n+1}{\in}I{\backslash}{\phi}(I)$, either $a_1,a_2,{\cdots},a_n{\in}I$ or the product of $a_{n+1}$ with (n-1) of $a_1,{\cdots},a_n$ is in $\sqrt{I}$. The aim of this paper is to investigate the concept of ${\phi}$-n-absorbing primary ideals.

#### Keywords

n-absorbing ideals;n-absorbing primary ideals;${\phi}$-n-absorbing primary ideals

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#### Cited by

1. Weakly Classical Prime Submodules vol.56, pp.4, 2016, https://doi.org/10.5666/KMJ.2016.56.4.1085