I-prime ideals

	I-prime ideals
Journal of Algebra and Related Topics
مقاله 5، دوره 4، شماره 2، اسفند 2016، صفحه 41-47 اصل مقاله (227.16 K)
نوع مقاله: Research Paper
نویسنده
I. Akray^*
Soran University
چکیده
In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b \in R$ with $ab \in P-IP$ implies either $a \in P$ or $b \in P$. We give some characterizations of $I$-prime ideals and study some of its properties. Moreover, we give conditions under which $I$-prime ideals becomes prime or weakly prime and we construct the view of $I$-prime ideal in decomposite rings.
کلیدواژه‌ها
prime ideal؛ weakly prime ideal؛ almost prime ideal؛ radical of the ideal

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