Pasting topological spaces at one point

Ali Rezaei Aliabad

Displaying similar documents to “Pasting topological spaces at one point”

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...

Intersections of essential minimal prime ideals

A. Taherifar (2014)

Commentationes Mathematicae Universitatis Carolinae

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Let $𝒵 (ℛ)$ be the set of zero divisor elements of a commutative ring $R$ with identity and $ℳ$ be the space of minimal prime ideals of $R$ with Zariski topology. An ideal $I$ of $R$ is called strongly dense ideal or briefly $s d$ -ideal if $I \subseteq 𝒵 (ℛ)$ and $I$ is contained in no minimal prime ideal. We denote by $R_{K} (ℳ)$ , the set of all $a \in R$ for which $\bar{D (a)} = \bar{ℳ ∖ V (a)}$ is compact. We show that $R$ has property $(A)$ and $ℳ$ is compact if and only if $R$ has no $s d$ -ideal. It is proved that $R_{K} (ℳ)$ is an essential ideal (resp., $s d$ -ideal) if and only if $ℳ$ is an almost...

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...

Displaying similar documents to “Pasting topological spaces at one point”

Fixed-place ideals in commutative rings

Intersections of essential minimal prime ideals

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

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