Displaying similar documents to “Rothberger gaps in fragmented ideals”

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 ∞ case have a Denjoy-Carleman counterpart.

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 (" ≤ K ") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals for which ≤ K ⇒ ⊑ 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).

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.

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...

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...

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

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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...