A characterization of the meager ideal

Piotr Zakrzewski

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Displaying similar documents to “A characterization of the meager ideal”

Normal restrictions of the noncofinal ideal on $P_{κ} (λ)$

Pierre Matet (2013)

Fundamenta Mathematicae

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We discuss the problem of whether there exists a restriction of the noncofinal ideal on $P_{κ} (λ)$ that is normal.

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.

Two remarks on the maximal-ideal space of H $^{\infty}$

Stephen Scheinberg (2021)

Commentationes Mathematicae Universitatis Carolinae

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The topology of the maximal-ideal space of $H^{\infty}$ is discussed.

C(X) vs. C(X) modulo its socle

F. Azarpanah, O. A. S. Karamzadeh, S. Rahmati (2008)

Colloquium Mathematicae

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Let $C_{F} (X)$ be the socle of C(X). It is shown that each prime ideal in $C (X) / C_{F} (X)$ is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that $d i m (C (X) / C_{F} (X)) \geq d i m C (X)$ , where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points....

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 $0 \neq a b \in Q$ for some $a, b \in R$ , then $a^{2} \in Q$ or $b \in \sqrt{Q} .$ 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...

On the Noether exponent

Anna Stasica (2003)

Annales Polonici Mathematici

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We obtain, in a simple way, an estimate for the Noether exponent of an ideal I without embedded components (i.e. we estimate the smallest number μ such that ${(r a d I)}^{μ} \subset I$ ).

On the ideal class groups of the maximal real subfields of number fields with all roots of unity

Masato Kurihara (1999)

Journal of the European Mathematical Society

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In this paper, for a totally real number field $k$ we show the ideal class group of $k {(\cup_{n > 0} μ_{n})}^{+}$ is trivial. We also study the $p$ -component of the ideal class group of the cyclotomic $𝐙_{p}$ -extension.

An ideal characterization of when a subspace of certain Banach spaces has the metric compact approximation property

J. Cabello, E. Nieto (1998)

Studia Mathematica

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C.-M. Cho and W. B. Johnson showed that if a subspace E of $ℓ_{p}$ , 1 < p < ∞, has the compact approximation property, then K(E) is an M-ideal in ℒ(E). We prove that for every r,s ∈ ]0,1] with $r^{2} + s^{2} < 1$ , the James space can be provided with an equivalent norm such that an arbitrary subspace E has the metric compact approximation property iff there is a norm one projection P on ℒ(E)* with Ker P = K(E)⊥ satisfying ∥⨍∥ ≥ r∥Pf∥ + s∥φ - Pf∥ ∀⨍ ∈ ℒ(E)*. A similar result is proved for subspaces of...

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

Gülşen Ulucak, Ece Yetkin Çelikel (2020)

Czechoslovak Mathematical Journal

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Calculation of the avoiding ideal for $Σ^{1, 1}$

Tamás Terpai (2009)

Banach Center Publications

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We calculate the mapping $H * (B O; ℤ ₂) \to H * (K^{1, 0}; ℤ ₂)$ and obtain a generating system of its kernel. As a corollary, bounds on the codimension of fold maps from real projective spaces to Euclidean space are calculated and the rank of a singular bordism group is determined.

More on cardinal invariants of analytic $P$ -ideals

Barnabás Farkas, Lajos Soukup (2009)

Commentationes Mathematicae Universitatis Carolinae

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Given an ideal $ℐ$ on $ω$ let $𝔞 (ℐ)$ ( $\bar{𝔞} (ℐ)$ ) be minimum of the cardinalities of infinite (uncountable) maximal $ℐ$ -almost disjoint subsets of ${[ω]}^{ω}$ . We show that $𝔞 (ℐ_{h}) > ω$ if $ℐ_{h}$ is a summable ideal; but $𝔞 (𝒵_{\vec{μ}}) = ω$ for any tall density ideal $𝒵_{\vec{μ}}$ including the density zero ideal $𝒵$ . On the other hand, you have $𝔟 \leq \bar{𝔞} (ℐ)$ for any analytic $P$ -ideal $ℐ$ , and $\bar{𝔞} (𝒵_{\vec{μ}}) \leq 𝔞$ for each density ideal $𝒵_{\vec{μ}}$ . For each ideal $ℐ$ on $ω$ denote $𝔟_{ℐ}$ and $𝔡_{ℐ}$ the unbounding and dominating numbers of $〈 ω^{ω}, \leq_{ℐ} 〉$ where $f \leq_{ℐ} g$ iff ${n \in ω : f (n) > g (n)} \in ℐ$ . We show that $𝔟_{ℐ} = 𝔟$ and $𝔡_{ℐ} = 𝔡$ for each analytic $P$ -ideal $ℐ$ . Given a Borel...

Wild primes of a self-equivalence of a number field

Alfred Czogała, Beata Rothkegel (2014)

Acta Arithmetica

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Let K be a number field. Assume that the 2-rank of the ideal class group of K is equal to the 2-rank of the narrow ideal class group of K. Moreover, assume K has a unique dyadic prime and the class of is a square in the ideal class group of K. We prove that if ₁,...,ₙ are finite primes of K such that ∙ the class of $_{i}$ is a square in the ideal class group of K for every i ∈ 1,...,n, ∙ -1 is a local square at $_{i}$ for every nondyadic $_{i} \in ₁, . . ., ₙ$ , then ₁,...,ₙ is the wild set of some self-equivalence...

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 $e$ .

More remarks on the intersection ideal $ℳ \cap 𝒩$

Tomasz Weiss (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove in ZFC that every $ℳ \cap 𝒩$ additive set is $𝒩$ additive, thus we solve Problem 20 from paper [Weiss T., A note on the intersection ideal $ℳ \cap 𝒩$ , Comment. Math. Univ. Carolin. 54 (2013), no. 3, 437-445] in the negative.