Irreducibility of ideals in a one-dimensional analytically irreducible ring

Valentina Barucci; Faten Khouja

Displaying similar documents to “Irreducibility of ideals in a one-dimensional analytically irreducible ring”

On $a$ -Kasch spaces

Ali Akbar Estaji, Melvin Henriksen (2010)

Archivum Mathematicum

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If $X$ is a Tychonoff space, $C (X)$ its ring of real-valued continuous functions. In this paper, we study non-essential ideals in $C (X)$ . Let $a$ be a infinite cardinal, then $X$ is called $a$ -Kasch (resp. $\bar{a}$ -Kasch) space if given any ideal (resp. $z$ -ideal) $I$ with $gen (I) < a$ then $I$ is a non-essential ideal. We show that $X$ is an $ℵ_{0}$ -Kasch space if and only if $X$ is an almost $P$ -space and $X$ is an $ℵ_{1}$ -Kasch space if and only if $X$ is a pseudocompact and almost $P$ -space. Let $C_{F} (X)$ denote the socle of $C (X)$ . For a topological space...

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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Displaying similar documents to “Irreducibility of ideals in a one-dimensional analytically irreducible ring”

On a -Kasch spaces

Intersections of essential minimal prime ideals

Fixed-place ideals in commutative rings

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

On $a$ -Kasch spaces

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