Displaying similar documents to “Star-invertible ideals of integral domains”

On nonregular ideals and z ∘ -ideals in C ( X )

F. Azarpanah, M. Karavan (2005)

Czechoslovak Mathematical Journal

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The spaces X in which every prime z ∘ -ideal of C ( X ) is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces X , such as metric spaces, basically disconnected spaces and one-point compactifications of discrete spaces, every prime z ∘ -ideal in C ( X ) is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in C ( X ) a z ∘ -ideal? When is every nonregular (prime) z -ideal in C ( X ) a...

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 ∘ ∈ Min ( I ) is called irredundant with respect to I if I ≠ ⋂ P ∘ ≠ P ∈ 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 ∈ β X is a fixed-place point if O p ( X ) is a fixed-place ideal. In...

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 ⊆ 𝒵 ( ℛ ) and I is contained in no minimal prime ideal. We denote by R K ( ℳ ) , the set of all a ∈ R for which D ( a ) ¯ = 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 ∈ Λ be a family of topological spaces and x α ∈ X α , for every α ∈ 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)...