Intersections of minimal prime ideals in the rings of continuous functions

Swapan Kumar Ghosh

Displaying similar documents to “Intersections of minimal prime ideals in the rings of continuous functions”

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...

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)...

On prime ideals of $C (X)$

Attilio Le Donne (1977)

Rendiconti del Seminario Matematico della Università di Padova

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Displaying similar documents to “Intersections of minimal prime ideals in the rings of continuous functions”

Intersections of essential minimal prime ideals

Pasting topological spaces at one point

On prime ideals of C ( X )

On prime ideals of $C (X)$