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All rings are commutative with $1\neq0$ and $n$ is a positive integer. Let $\phi:\mathfrak{J}(R)\rightarrow \mathfrak{J}(R)\cup\{\emptyset\}$ be a function where $\mathfrak{J}(R)$ denotes the set of all ideals of $R$. We say that a proper ideal $I$ of $R$ is {\it $\phi$-$n$-absorbing primary} if whenever $a_1,a_2,\dots,a_{n+1}\in R$ 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 $a_1,\dots,a_n$ is in $\sqrt{I}$. The aim of this paper is to investigate the concept of $\phi$-$n$-absorbing primary ideals.
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참고문헌 (25)
참고문헌 신청
D. D. Anderson / 2008 / Generalizations of prime ideals / Comm. Algebra 36(2):686~696
D. D. Anderson / 2003 / Weakly prime ideals / Houston J. Math 29(4):831~840
D. F. Anderson / 2011 / On n-absorbing ideals of commutative rings / Comm. Algebra 39(5):1646~1672
A. Badawi / 2007 / On 2-absorbing ideals of commutative rings / Bull. Austral. Math. Soc 75(3):417~429
A. Badawi / 2002 / Powerful ideals, strongly primary ideals, almost pseudovaluation domains, and conducive domains / Comm. Algebra 30(4):1591~1606
D. D. Anderson / 2003 / Weakly prime ideals / Houston J. Math 29(4):831~840
D. F. Anderson / 2011 / On n-absorbing ideals of commutative rings / Comm. Algebra 39(5):1646~1672
A. Badawi / 2007 / On 2-absorbing ideals of commutative rings / Bull. Austral. Math. Soc 75(3):417~429
A. Badawi / 2002 / Powerful ideals, strongly primary ideals, almost pseudovaluation domains, and conducive domains / Comm. Algebra 30(4):1591~1606
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