Pseudo-valuation rings. II

David F. Anderson; Ayman Badawi; David E. Dobbs

Displaying similar documents to “Pseudo-valuation rings. II”

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.

Isolated points and redundancy

P. Alirio J. Peña, Jorge E. Vielma (2011)

Commentationes Mathematicae Universitatis Carolinae

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We describe the isolated points of an arbitrary topological space $(X, τ)$ . If the $τ$ -specialization pre-order on $X$ has enough maximal elements, then a point $x \in X$ is an isolated point in $(X, τ)$ if and only if $x$ is both an isolated point in the subspaces of $τ$ -kerneled points of $X$ and in the $τ$ -closure of ${x}$ (a special case of this result is proved in Mehrvarz A.A., Samei K., , J. Sci. Islam. Repub. Iran (1999), no. 3, 193–196). This result is applied to an arbitrary subspace of the prime spectrum $Spec (R)$ of...