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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If N is a nontrivial proper normal subgroup of a finite group G then N and G/N are smaller than G. While it is false that G can be completely reconstructed from knowledge of N and G/N (see Example 1.1 below), it is nevertheless a standard technique in finite group theory to prove theorems about finite groups by induction on the size of the group and thereby use information about the smaller gro...
متن کاملi-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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In this article, we have characterized ideals in $C(X)$ in which every ideal is also an ideal (a $z$-ideal) of $C(X)$. Motivated by this characterization, we observe that $C_infty(X)$ is a regular ring if and only if every open locally compact $sigma$-compact subset of $X$ is finite. Concerning prime ideals, it is shown that the sum of every two prime (semiprime) ideals of e...
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We describe a recipe for generating normal ideals on successors of singular cardinals. We show that these ideals are related to many weakenings of that have appeared in the literature. Our main purpose, however, is to provide an organized list of open questions related to these ideals. Throughout this note, we will let λ denote the successor of a singular cardinal μ. We will also let χ denote s...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1983
ISSN: 0022-4049
DOI: 10.1016/0022-4049(83)90061-0