Displaying similar documents to “Erratum to ( δ , 2 ) -primary ideals of a commutative ring”

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...

Characterization of irreducible polynomials over a special principal ideal ring

Brahim Boudine (2023)

Mathematica Bohemica

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A commutative ring R with unity is called a special principal ideal ring (SPIR) if it is a non integral principal ideal ring containing only one nonzero prime ideal, its length e is the index of nilpotency of its maximal ideal. In this paper, we show a characterization of irreducible polynomials over a SPIR of length 2 . Then, we give a sufficient condition for a polynomial to be irreducible over a SPIR of any length e .

On wsq-primary ideals

Emel Aslankarayiğit Uğurlu, El Mehdi Bouba, Ünsal Tekir, Suat Koç (2023)

Czechoslovak Mathematical Journal

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We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let R be a commutative ring with a nonzero identity and Q a proper ideal of R . The proper ideal Q is said to be a weakly strongly quasi-primary ideal if whenever 0 ≠ a b ∈ Q for some a , b ∈ R , then a 2 ∈ Q or b ∈ Q . Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero...

The ideal (a) is not G δ generated

Marta Frankowska, Andrzej Nowik (2011)

Colloquium Mathematicae

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We prove that the ideal (a) defined by the density topology is not G δ generated. This answers a question of Z. Grande and E. Strońska.

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...

Rings of continuous functions vanishing at infinity

Ali Rezaei Aliabad, F. Azarpanah, M. Namdari (2004)

Commentationes Mathematicae Universitatis Carolinae

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We prove that a Hausdorff space X is locally compact if and only if its topology coincides with the weak topology induced by C ∞ ( X ) . It is shown that for a Hausdorff space X , there exists a locally compact Hausdorff space Y such that C ∞ ( X ) ≅ C ∞ ( Y ) . It is also shown that for locally compact spaces X and Y , C ∞ ( X ) ≅ C ∞ ( Y ) if and only if X ≅ Y . Prime ideals in C ∞ ( X ) are uniquely represented by a class of prime ideals in C * ( X ) . ∞ -compact spaces are introduced and it turns out that a locally compact space X is ∞ -compact if and only...