i-prime ideals
نویسندگان
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.
منابع مشابه
I-prime ideals
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 ...
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عنوان ژورنال:
journal of algebra and related topicsجلد ۴، شماره ۲، صفحات ۴۱-۴۷
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