Stronger ideals over $_{κ}λ $

Yo Matsubara

Displaying similar documents to “Stronger ideals over $_{κ} λ$ ”

When does the Katětov order imply that one ideal extends the other?

Paweł Barbarski, Rafał Filipów, Nikodem Mrożek, Piotr Szuca (2013)

Colloquium Mathematicae

Similarity:

We consider the Katětov order between ideals of subsets of natural numbers (" $\leq_{K}$ ") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals for which $\leq_{K} \Rightarrow ⊑$ for every ideal . We find examples of ideals with this property and show how this property can be used to reformulate some problems known from the literature in terms of the Katětov order instead of the order "⊑ " (and vice versa).

Invertible ideals and Gaussian semirings

Shaban Ghalandarzadeh, Peyman Nasehpour, Rafieh Razavi (2017)

Archivum Mathematicum

Similarity:

In the first section, we introduce the notions of fractional and invertible ideals of semirings and characterize invertible ideals of a semidomain. In section two, we define Prüfer semirings and characterize them in terms of valuation semirings. In this section, we also characterize Prüfer semirings in terms of some identities over its ideals such as $(I + J) (I \cap J) = I J$ for all ideals $I$ , $J$ of $S$ . In the third section, we give a semiring version for the Gilmer-Tsang Theorem, which states that for a suitable...

Łojasiewicz ideals in Denjoy-Carleman classes

Vincent Thilliez (2013)

Studia Mathematica

Similarity:

The classical notion of Łojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of Łojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual Łojasiewicz inequality. We then show that basic properties of Łojasiewicz ideals in the $^{\infty}$ case have a Denjoy-Carleman counterpart.

On the associated prime ideals of local cohomology modules defined by a pair of ideals

Maryam Jahangiri, Zohreh Habibi, Khadijeh Ahmadi Amoli (2016)

Discussiones Mathematicae General Algebra and Applications

Similarity:

Let I and J be two ideals of a commutative Noetherian ring R and M be an R-module. For a non-negative integer n it is shown that, if the sets $A s s_{R} (E x t_{R}^{n} (R / I, M))$ and $S u p p_{R} (E x t_{R}^{i} (R / I, H_{I, J}^{j} (M)))$ are finite for all i ≤ n+1 and all j < n, then so is $A s s_{R} (H o m_{R} (R / I, H_{I, J}^{n} (M)))$ . We also study the finiteness of $A s s_{R} (E x t_{R}^{i} (R / I, H_{I, J}^{n} (M)))$ for i = 1,2.

Weak Rudin-Keisler reductions on projective ideals

Konstantinos A. Beros (2016)

Fundamenta Mathematicae

Similarity:

We consider a slightly modified form of the standard Rudin-Keisler order on ideals and demonstrate the existence of complete (with respect to this order) ideals in various projective classes. Using our methods, we obtain a simple proof of Hjorth’s theorem on the existence of a complete Π¹₁ equivalence relation. This proof enables us (under PD) to generalize Hjorth’s result to the classes of $Π ¹_{2 n + 1}$ equivalence relations.

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...

Monomial ideals with tiny squares and Freiman ideals

Ibrahim Al-Ayyoub, Mehrdad Nasernejad (2021)

Czechoslovak Mathematical Journal

Similarity:

We provide a construction of monomial ideals in $R = K [x, y]$ such that $μ (I^{2}) < μ (I)$ , where $μ$ denotes the least number of generators. This construction generalizes the main result of S. Eliahou, J. Herzog, M. Mohammadi Saem (2018). Working in the ring $R$ , we generalize the definition of a Freiman ideal which was introduced in J. Herzog, G. Zhu (2019) and then we give a complete characterization of such ideals. A particular case of this characterization leads to some further investigations on $μ (I^{k})$ that generalize...

Monomial ideals with 3-linear resolutions

Marcel Morales, Abbas Nasrollah Nejad, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

In this paper, we study the Castelnuovo-Mumford regularity of square-free monomial ideals generated in degree $3$ . We define some operations on the clutters associated to such ideals and prove that the regularity is preserved under these operations. We apply these operations to introduce some classes of ideals with linear resolutions and also show that any clutter corresponding to a triangulation of the sphere does not have linear resolution while any proper subclutter of it has a linear...

Erratum to “Can $ℬ (ℓ^{p})$ ever be amenable?” (Studia Math. 188 (2008), 151-174)

Matthew Daws, Volker Runde (2009)

Studia Mathematica

Similarity:

Rothberger gaps in fragmented ideals

Jörg Brendle, Diego Alejandro Mejía (2014)

Fundamenta Mathematicae

Similarity:

The Rothberger number (ℐ) of a definable ideal ℐ on ω is the least cardinal κ such that there exists a Rothberger gap of type (ω,κ) in the quotient algebra (ω)/ℐ. We investigate (ℐ) for a class of $F_{σ}$ ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is ℵ₁, while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even...

Semiproper ideals

Hiroshi Sakai (2005)

Fundamenta Mathematicae

Similarity:

We say that an ideal I on $_{κ} λ$ is semiproper if the corresponding poset $ℙ_{I}$ is semiproper. In this paper we investigate properties of semiproper ideals on $_{κ} λ$ .

On domains with ACC on invertible ideals

Stefania Gabelli (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

If $A$ is a domain with the ascending chain condition on (integral) invertible ideals, then the group $I(A)$ of its invertible ideals is generated by the set $I_{m}(A)$ of maximal invertible ideals. In this note we study some properties of $I_{m}(A)$ and we prove that, if $I(A)$ is a free group on $I_{m}(A)$ , then $A$ is a locally factorial Krull domain.

On quasi $n$ -ideals of commutative rings

Adam Anebri, Najib Mahdou, Emel Aslankarayiğit Uğurlu (2022)

Czechoslovak Mathematical Journal

Similarity:

Let $R$ be a commutative ring with a nonzero identity. In this study, we present a new class of ideals lying properly between the class of $n$ -ideals and the class of $(2, n)$ -ideals. A proper ideal $I$ of $R$ is said to be a quasi $n$ -ideal if $\sqrt{I}$ is an $n$ -ideal of $R .$ Many examples and results are given to disclose the relations between this new concept and others that already exist, namely, the $n$ -ideals, the quasi primary ideals, the $(2, n)$ -ideals and the $p r$ -ideals. Moreover, we use the quasi $n$ -ideals to characterize...

Transitive Properties of Ideals on Generalized Cantor Spaces

Jan Kraszewski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We compute transitive cardinal coefficients of ideals on generalized Cantor spaces. In particular, we show that there exists a null set $A \subseteq 2^{ω ₁}$ such that for every null set $B \subseteq 2^{ω ₁}$ we can find $x \in 2^{ω ₁}$ such that A ∪ (A+x) cannot be covered by any translation of B.

The reaping and splitting numbers of nice ideals

Rafał Filipów (2014)

Colloquium Mathematicae

Similarity:

We examine the splitting number (B) and the reaping number (B) of quotient Boolean algebras B = (ω)/ℐ where ℐ is an $F_{σ}$ ideal or an analytic P-ideal. For instance we prove that under Martin’s Axiom ((ω)/ℐ) = for all $F_{σ}$ ideals ℐ and for all analytic P-ideals ℐ with the BW property (and one cannot drop the BW assumption). On the other hand under Martin’s Axiom ((ω)/ℐ) = for all $F_{σ}$ ideals and all analytic P-ideals ℐ (in this case we do not need the BW property). We also provide applications...

Closed ideals in algebras of smooth functions

Hanin Leonid G.

Similarity:

AbstractA topological algebra admits spectral synthesis of ideals (SSI) if every closed ideal in this algebra is an intersection of closed primary ideals. According to classical results this is the case for algebras of continuous, several times continuously differentiable, and Lipschitz functions. New examples (and counterexamples) of function algebras that admit or fail to have SSI are presented. It is shown that the Sobolev algebra $W_{p}^{l} (ℝ ⁿ)$ , 1 ≤ p < ∞, has the property of SSI for and only...

On domains with ACC on invertible ideals

Stefania Gabelli (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

Bad properties of the Bernstein numbers

Albrecht Pietsch (2008)

Studia Mathematica

Similarity:

We show that the classes $_{p}^{b e r n} : = T : (b ₙ (T)) \in l_{p}$ associated with the Bernstein numbers bₙ fail to be operator ideals. Moreover, $_{p}^{b e r n} \circ_{q}^{b e r n} ⊈_{r}^{b e r n}$ for 1/r = 1/p + 1/q.

$0$ -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. ...

On ${(m, n)}_{T}$ ideals and subgroups of a semigroup

D. N. Krgović (1977)

Matematički Vesnik

Similarity:

Squarefree monomial ideals with maximal depth

Ahad Rahimi (2020)

Czechoslovak Mathematical Journal

Similarity:

Let $(R, 𝔪)$ be a Noetherian local ring and $M$ a finitely generated $R$ -module. We say $M$ has maximal depth if there is an associated prime $𝔭$ of $M$ such that depth $M = dim R / 𝔭$ . In this paper we study squarefree monomial ideals which have maximal depth. Edge ideals of cycle graphs, transversal polymatroidal ideals and high powers of connected bipartite graphs with this property are classified.

A graph associated to proper non-small ideals of a commutative ring

S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel (2017)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this paper, a new kind of graph on a commutative ring is introduced and investigated. Small intersection graph of a ring $R$ , denoted by $G (R)$ , is a graph with all non-small proper ideals of $R$ as vertices and two distinct vertices $I$ and $J$ are adjacent if and only if $I \cap J$ is not small in $R$ . In this article, some interrelation between the graph theoretic properties of this graph and some algebraic properties of rings are studied. We investigated the basic properties of the small intersection...

Displaying similar documents to “Stronger ideals over κ λ ”

Displaying similar documents to “Stronger ideals over $_{κ} λ$ ”