Rings of continuous functions vanishing at infinity

Ali Rezaei Aliabad; F. Azarpanah; M. Namdari

Displaying similar documents to “Rings of continuous functions vanishing at infinity”

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...

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...

Erratum to $(δ, 2)$ -primary ideals of a commutative ring

Gülşen Ulucak, Ece Yetkin Çelikel (2020)

Czechoslovak Mathematical Journal

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$C (X)$ can sometimes determine $X$ without $X$ being realcompact

Melvin Henriksen, Biswajit Mitra (2005)

Commentationes Mathematicae Universitatis Carolinae

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As usual $C (X)$ will denote the ring of real-valued continuous functions on a Tychonoff space $X$ . It is well-known that if $X$ and $Y$ are realcompact spaces such that $C (X)$ and $C (Y)$ are isomorphic, then $X$ and $Y$ are homeomorphic; that is $C (X)$ $X$ . The restriction to realcompact spaces stems from the fact that $C (X)$ and $C (υ X)$ are isomorphic, where $υ X$ is the (Hewitt) realcompactification of $X$ . In this note, a class of locally compact spaces $X$ that includes properly the class of locally...

Displaying similar documents to “Rings of continuous functions vanishing at infinity”

Intersections of essential minimal prime ideals

Fixed-place ideals in commutative rings

Erratum to ( δ , 2 ) -primary ideals of a commutative ring

C ( X ) can sometimes determine X without X being realcompact

Erratum to $(δ, 2)$ -primary ideals of a commutative ring

$C (X)$ can sometimes determine $X$ without $X$ being realcompact