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http://dx.doi.org/10.4134/JKMS.j150171

ON 𝜙-n-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS  

Mostafanasab, Hojjat (Department of Mathematics and Applications University of Mohaghegh Ardabili)
Darani, Ahmad Yousefian (Department of Mathematics and Applications University of Mohaghegh Ardabili)
Publication Information
Journal of the Korean Mathematical Society / v.53, no.3, 2016 , pp. 549-582 More about this Journal
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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