The ideal (a) is not $G_δ$ generated

Marta Frankowska; Andrzej Nowik

Displaying similar documents to “The ideal (a) is not $G_{δ}$ generated”

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

Pierre Matet (2013)

Fundamenta Mathematicae

Similarity:

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

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

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

Colloquium Mathematicae

Similarity:

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....

A characterization of the meager ideal

Piotr Zakrzewski (2015)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We give a classical proof of the theorem stating that the $σ$ -ideal of meager sets is the unique $σ$ -ideal on a Polish group, generated by closed sets which is invariant under translations and ergodic.

On the Noether exponent

Anna Stasica (2003)

Annales Polonici Mathematici

Similarity:

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 ${(r a d I)}^{μ} \subset I$ ).

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

Tamás Terpai (2009)

Banach Center Publications

Similarity:

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.

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

Similarity:

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.

A co-ideal based identity-summand graph of a commutative semiring

S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel (2015)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let $I$ be a strong co-ideal of a commutative semiring $R$ with identity. Let $Γ_{I} (R)$ be a graph with the set of vertices $S_{I} (R) = {x \in R ∖ I : x + y \in I$ for some $y \in R ∖ I}$ , where two distinct vertices $x$ and $y$ are adjacent if and only if $x + y \in I$ . We look at the diameter and girth of this graph. Also we discuss when $Γ_{I} (R)$ is bipartite. Moreover, studies are done on the planarity, clique, and chromatic number of this graph. Examples illustrating the results are presented.

Wild primes of a self-equivalence of a number field

Alfred Czogała, Beata Rothkegel (2014)

Acta Arithmetica

Similarity:

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...

More on the strongly 1-absorbing primary ideals of commutative rings

Ali Yassine, Mohammad Javad Nikmehr, Reza Nikandish (2024)

Czechoslovak Mathematical Journal

Similarity:

Let $R$ be a commutative ring with identity. We study the concept of strongly 1-absorbing primary ideals which is a generalization of $n$ -ideals and a subclass of $1$ -absorbing primary ideals. A proper ideal $I$ of $R$ is called strongly 1-absorbing primary if for all nonunit elements $a, b, c \in R$ such that $a b c \in I$ , it is either $a b \in I$ or $c \in \sqrt{0}$ . Some properties of strongly 1-absorbing primary ideals are studied. Finally, rings $R$ over which every semi-primary ideal is strongly 1-absorbing primary, and rings $R$ over which...

Eigenspaces of the ideal class group

Cornelius Greither, Radan Kučera (2014)

Annales de l’institut Fourier

Similarity:

The aim of this paper is to prove an analog of Gras’ conjecture for an abelian field $F$ and an odd prime $p$ dividing the degree $[F : ℚ]$ assuming that the $p$ -part of $Gal (F / ℚ)$ group is cyclic.

Duality of measures of non-𝒜-compactness

Juan Manuel Delgado, Cándido Piñeiro (2015)

Studia Mathematica

Similarity:

Let be a Banach operator ideal. Based on the notion of -compactness in a Banach space due to Carl and Stephani, we deal with the notion of measure of non–compactness of an operator. We consider a map $χ_{}$ (respectively, $n_{}$ ) acting on the operators of the surjective (respectively, injective) hull of such that $χ_{} (T) = 0$ (respectively, $n_{} (T) = 0$ ) if and only if the operator T is -compact (respectively, injectively -compact). Under certain conditions on the ideal , we prove an equivalence inequality involving...

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

J. Cabello, E. Nieto (1998)

Studia Mathematica

Similarity:

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...

M-ideals of homogeneous polynomials

Verónica Dimant (2011)

Studia Mathematica

Similarity:

We study the problem of whether $_{w} (ⁿ E)$ , the space of n-homogeneous polynomials which are weakly continuous on bounded sets, is an M-ideal in the space (ⁿE) of continuous n-homogeneous polynomials. We obtain conditions that ensure this fact and present some examples. We prove that if $_{w} (ⁿ E)$ is an M-ideal in (ⁿE), then $_{w} (ⁿ E)$ coincides with $_{w 0} (ⁿ E)$ (n-homogeneous polynomials that are weakly continuous on bounded sets at 0). We introduce a polynomial version of property (M) and derive that if $_{w} (ⁿ E) =_{w 0} (ⁿ E)$ and (E) is an...

$0$ -ideals in $0$ -distributive posets

Khalid A. Mokbel (2016)

Mathematica Bohemica

Similarity:

The concept of a $0$ -ideal in $0$ -distributive posets is introduced. Several properties of $0$ -ideals in $0$ -distributive posets are established. Further, the interrelationships between $0$ -ideals and $α$ -ideals in $0$ -distributive posets are investigated. Moreover, a characterization of prime ideals to be $0$ -ideals in $0$ -distributive posets is obtained in terms of non-dense ideals. It is shown that every $0$ -ideal of a $0$ -distributive meet semilattice is semiprime. Several counterexamples are discussed. ...

$α$ -ideals in $0$ -distributive posets

Khalid A. Mokbel (2015)

Mathematica Bohemica

Similarity:

The concept of $α$ -ideals in posets is introduced. Several properties of $α$ -ideals in $0$ -distributive posets are studied. Characterization of prime ideals to be $α$ -ideals in $0$ -distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal $I$ of a $0$ -distributive poset is non-dense, then $I$ is an $α$ -ideal. Moreover, it is shown that the set of all $α$ -ideals $α Id (P)$ of a poset $P$ with $0$ forms a complete lattice. A result analogous to separation theorem for...

On norm closed ideals in $L (ℓ_{p}, ℓ_{q})$

B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, V. G. Troitsky (2007)

Studia Mathematica

Similarity:

It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for $X = ℓ_{p}$ (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of $L (ℓ_{p} \oplus ℓ_{q})$ for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in $L (ℓ_{p}, ℓ_{q})$ for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in $L (ℓ_{p}, ℓ_{q})$ , including one that has not been studied before. The proofs use various methods...

The strong persistence property and symbolic strong persistence property

Mehrdad Nasernejad, Kazem Khashyarmanesh, Leslie G. Roberts, Jonathan Toledo (2022)

Czechoslovak Mathematical Journal

Similarity:

Let $I$ be an ideal in a commutative Noetherian ring $R$ . Then the ideal $I$ has the strong persistence property if and only if $(I^{k + 1} :_{R} I) = I^{k}$ for all $k$ , and $I$ has the symbolic strong persistence property if and only if $(I^{(k + 1)} :_{R} I^{(1)}) = I^{(k)}$ for all $k$ , where $I^{(k)}$ denotes the $k$ th symbolic power of $I$ . We study the strong persistence property for some classes of monomial ideals. In particular, we present a family of primary monomial ideals failing the strong persistence property. Finally, we show that every square-free monomial...

Corrigendum to “Commutators on ${(\sum ℓ_{q})}_{p}$ ” (Studia Math. 206 (2011), 175-190)

Dongyang Chen, William B. Johnson, Bentuo Zheng (2014)

Studia Mathematica

Similarity:

We give a corrected proof of Theorem 2.10 in our paper “Commutators on ${(\sum ℓ_{q})}_{p}$ ” [Studia Math. 206 (2011), 175-190] for the case 1 < q < p < ∞. The case when 1 = q < p < ∞ remains open. As a consequence, the Main Theorem and Corollary 2.17 in that paper are only valid for 1 < p,q < ∞.

Ideals in big Lipschitz algebras of analytic functions

Thomas Vils Pedersen (2004)

Studia Mathematica

Similarity:

For 0 < γ ≤ 1, let $Λ ⁺_{γ}$ be the big Lipschitz algebra of functions analytic on the open unit disc which satisfy a Lipschitz condition of order γ on ̅. For a closed set E on the unit circle and an inner function Q, let $J_{γ} (E, Q)$ be the closed ideal in $Λ ⁺_{γ}$ consisting of those functions $f \in Λ ⁺_{γ}$ for which (i) f = 0 on E, (ii) $| f (z) - f (w) | = o (| z - w |^{γ})$ as d(z,E),d(w,E) → 0, (iii) $f / Q \in Λ ⁺_{γ}$ . Also, for a closed ideal I in $Λ ⁺_{γ}$ , let $E_{I}$ = z ∈ : f(z) = 0 for every f ∈ I and let $Q_{I}$ be the greatest common divisor of the inner parts of non-zero functions...

Some generalizations of Olivier's theorem

Alain Faisant, Georges Grekos, Ladislav Mišík (2016)

Mathematica Bohemica

Similarity:

Let $\sum_{n = 1}^{\infty} a_{n}$ be a convergent series of positive real numbers. L. Olivier proved that if the sequence $(a_{n})$ is non-increasing, then $lim_{n \to \infty} n a_{n} = 0$ . In the present paper: (a) We formulate and prove a necessary and sufficient condition for having $lim_{n \to \infty} n a_{n} = 0$ ; Olivier’s theorem is a consequence of our Theorem . (b) We prove properties analogous to Olivier’s property when the usual convergence is replaced by the $ℐ$ -convergence, that is a convergence according to an ideal $ℐ$ of subsets of $ℕ$ . Again, Olivier’s theorem is a consequence...

Displaying similar documents to “The ideal (a) is not G δ generated”

Displaying similar documents to “The ideal (a) is not $G_{δ}$ generated”