On \phi-n-absorbing primary ideals of commutative rings

28 Feb 2015  ·  Mostafanasab Hojjat, Darani Ahmad Yousefian ·

All rings are commutative with $1$ and $n$ is a positive integer. Let $\phi: J(R)\to J(R)\cup{\emptyset}$ be a function where $J(R)$ denotes the set of all ideals of $R$... We say that a proper ideal $I$ of $R$ is $\phi$-$n$-absorbing primary if whenever $a_1,a_2,...,a_{n+1}\in R$ and $a_1a_2\cdots a_{n+1}\in I\backslash\phi(I)$, either $a_1a_2\cdots a_n\in I$ 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 $\phi$-$n$-absorbing primary ideals. read more

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Commutative Algebra