Intersections of essential minimal prime ideals

A. Taherifar

Displaying similar documents to “Intersections of essential minimal prime ideals”

Fixed-place ideals in commutative rings

Ali Rezaei Aliabad, Mehdi Badie (2013)

Commentationes Mathematicae Universitatis Carolinae

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Let $I$ be a semi-prime ideal. Then $P_{\circ} \in Min (I)$ is called irredundant with respect to $I$ if $I \neq ⋂_{P_{\circ} \neq P \in Min (I)} P$ . If $I$ is the intersection of all irredundant ideals with respect to $I$ , it is called a fixed-place ideal. If there are no irredundant ideals with respect to $I$ , it is called an anti fixed-place ideal. We show that each semi-prime ideal has a unique representation as an intersection of a fixed-place ideal and an anti fixed-place ideal. We say the point $p \in β X$ is a fixed-place point if $O^{p} (X)$ is a fixed-place ideal. In...

On nonregular ideals and $z^{\circ}$ -ideals in $C (X)$

F. Azarpanah, M. Karavan (2005)

Czechoslovak Mathematical Journal

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The spaces $X$ in which every prime $z^{\circ}$ -ideal of $C (X)$ is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces $X$ , such as metric spaces, basically disconnected spaces and one-point compactifications of discrete spaces, every prime $z^{\circ}$ -ideal in $C (X)$ is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in $C (X)$ a $z^{\circ}$ -ideal? When is every nonregular (prime) $z$ -ideal in $C (X)$ a...

Pasting topological spaces at one point

Ali Rezaei Aliabad (2006)

Czechoslovak Mathematical Journal

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Let ${X_{α}}_{α \in Λ}$ be a family of topological spaces and $x_{α} \in X_{α}$ , for every $α \in Λ$ . Suppose $X$ is the quotient space of the disjoint union of $X_{α}$ ’s by identifying $x_{α}$ ’s as one point $σ$ . We try to characterize ideals of $C (X)$ according to the same ideals of $C (X_{α})$ ’s. In addition we generalize the concept of rank of a point, see [9], and then answer the following two algebraic questions. Let $m$ be an infinite cardinal. (1) Is there any ring $R$ and $I$ an ideal in $R$ such that $I$ is an irreducible intersection of $m$ prime ideals? (2)...

Displaying similar documents to “Intersections of essential minimal prime ideals”

Fixed-place ideals in commutative rings

On nonregular ideals and z ∘ -ideals in C ( X )

Pasting topological spaces at one point

On nonregular ideals and $z^{\circ}$ -ideals in $C (X)$