ON 𝜙-n-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS

Title & Authors
ON 𝜙-n-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS

Abstract
All rings are commutative with $\small{1{\neq}0}$ and n is a positive integer. Let $\small{{\phi}:{\Im}(R){\rightarrow}{\Im}(R){\cup}\{{\emptyset}\}}$ be a function where $\small{{\Im}(R)}$ denotes the set of all ideals of R. We say that a proper ideal I of R is $\small{{\phi}}$-n-absorbing primary if whenever $\small{a_1,a_2,{\cdots},a_{n+1}{\in}R}$ and $\small{a_1,a_2,{\cdots},a_{n+1}{\in}I{\backslash}{\phi}(I)}$, either $\small{a_1,a_2,{\cdots},a_n{\in}I}$ or the product of $\small{a_{n+1}}$ with (n-1) of $\small{a_1,{\cdots},a_n}$ is in $\small{\sqrt{I}}$. The aim of this paper is to investigate the concept of $\small{{\phi}}$-n-absorbing primary ideals.
Keywords
n-absorbing ideals;n-absorbing primary ideals;$\small{{\phi}}$-n-absorbing primary ideals;
Language
English
Cited by
1.
Weakly Classical Prime Submodules, Kyungpook mathematical journal, 2016, 56, 4, 1085
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