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

F. Azarpanah; M. Karavan

Displaying similar documents to “On nonregular ideals and $z^{\circ}$ -ideals in $C (X)$ ”

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...

Star-invertible ideals of integral domains

Gyu Whan Chang, Jeanam Park (2003)

Bollettino dell'Unione Matematica Italiana

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Let $*$ be a star-operation on $R$ and $*_{s}$ the finite character star-operation induced by $*$ . The purpose of this paper is to study when $* = v$ or $*_{s} = t$ . In particular, we prove that if every prime ideal of $R$ is $*$ -invertible, then $* = v$ , and that if $R$ is a unique $*$ -factorable domain, then $R$ is a Krull domain.

Displaying similar documents to “On nonregular ideals and z ∘ -ideals in C ( X ) ”

Intersections of essential minimal prime ideals

Fixed-place ideals in commutative rings

Star-invertible ideals of integral domains

Displaying similar documents to “On nonregular ideals and $z^{\circ}$ -ideals in $C (X)$ ”