Monomial ideals with 3-linear resolutions

Marcel Morales; Abbas Nasrollah Nejad; Ali Akbar Yazdan Pour; Rashid Zaare-Nahandi

Displaying similar documents to “Monomial ideals with 3-linear resolutions”

Łojasiewicz ideals in Denjoy-Carleman classes

Vincent Thilliez (2013)

Studia Mathematica

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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.

Stronger ideals over $_{κ} λ$

Yo Matsubara (2002)

Fundamenta Mathematicae

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In §1 we define some properties of ideals by using games. These properties strengthen precipitousness. We call these stronger ideals. In §2 we show some limitations on the existence of such ideals over $_{κ} λ$ . We also present a consistency result concerning the existence of such ideals over $_{κ} λ$ . In §3 we show that such ideals satisfy stronger normality. We show a cardinal arithmetical consequence of the existence of strongly normal ideals. In § 4 we study some “large cardinal-like” consequences...

Rothberger gaps in fragmented ideals

Jörg Brendle, Diego Alejandro Mejía (2014)

Fundamenta Mathematicae

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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...

Weak Rudin-Keisler reductions on projective ideals

Konstantinos A. Beros (2016)

Fundamenta Mathematicae

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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.

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

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

Colloquium Mathematicae

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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).

Filtrations by Complete Ideals and Applications

E. Casas Alvero (1993)

Cours de l'institut Fourier

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Some new ideals of sets on the real line

Jan Mycielski (1969)

Colloquium Mathematicae

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Non-linear maps preserving ideals on a parabolic subalgebra of a simple algebra

Deng Yin Wang, Haishan Pan, Xuansheng Wang (2010)

Czechoslovak Mathematical Journal

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Let $𝒫$ be an arbitrary parabolic subalgebra of a simple associative $F$ -algebra. The ideals of $𝒫$ are determined completely; Each ideal of $𝒫$ is shown to be generated by one element; Every non-linear invertible map on $𝒫$ that preserves ideals is described in an explicit formula.

A note on unions of ideals and cosets of ideals.

Zandt, Michael (1995)

Beiträge zur Algebra und Geometrie

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Structural properties of ideals

J. E. Baumgartner, A. D. Taylor, S. Wagon

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CONTENTSPreface.............................................................................................. 5Chapter I. Preliminaries................................................................. 61. Notation and terminology.......................................................... 62. Results from the literature......................................................... 93. Definitions and basic properties.............................................. 11Chapter II. Subnormality and...

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

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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.

A characterization of F-algebras with all one-sided ideals closed

W. Żelazko (2005)

Studia Mathematica

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We prove that a real or complex F-algebra has all left and right ideals closed if and only if it is noetherian.

Combinatorics of ideals --- selectivity versus density

A. Kwela, P. Zakrzewski (2017)

Commentationes Mathematicae Universitatis Carolinae

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This note is devoted to combinatorial properties of ideals on the set of natural numbers. By a result of Mathias, two such properties, selectivity and density, in the case of definable ideals, exclude each other. The purpose of this note is to measure the ``distance'' between them with the help of ultrafilter topologies of Louveau.

On isomorphisms between $σ$ -ideals on $ω_{1}$

Marek Balcerzak (1990)

Commentationes Mathematicae Universitatis Carolinae

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Non-standard characterisations of ideals in C(X).

Jeppe Christoffer Dyre (1982)

Mathematica Scandinavica

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Closed ideals in algebras of smooth functions

Hanin Leonid G.

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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...