Semiproper ideals
Hiroshi Sakai (2005)
Fundamenta Mathematicae
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We say that an ideal I on is semiproper if the corresponding poset is semiproper. In this paper we investigate properties of semiproper ideals on .
Hiroshi Sakai (2005)
Fundamenta Mathematicae
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We say that an ideal I on is semiproper if the corresponding poset is semiproper. In this paper we investigate properties of semiproper ideals on .
Stefania Gabelli (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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If is a domain with the ascending chain condition on (integral) invertible ideals, then the group of its invertible ideals is generated by the set of maximal invertible ideals. In this note we study some properties of and we prove that, if is a free group on , then is a locally factorial Krull domain.
P. Dodos, J. Lopez-Abad, S. Todorcevic (2012)
Fundamenta Mathematicae
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Motivated by an application to the unconditional basic sequence problem appearing in our previous paper, we introduce analogues of the Laver ideal on ℵ₂ living on index sets of the form and use this to refine the well-known high-dimensional polarized partition relation for of Shelah.
János Kollár (1999)
Journal of the European Mathematical Society
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Let be polynomials in variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials such that . The effective versions of this result bound the degrees of the in terms of the degrees of the . The aim of this paper is to generalize this to the case when the are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.
B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, V. G. Troitsky (2007)
Studia Mathematica
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It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in , including one that has not been studied before. The proofs use various methods...
Lingli Zeng, Jizhu Nan (2016)
Czechoslovak Mathematical Journal
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Let be a finite field of characteristic and a field which contains a primitive th root of unity and . Suppose that a classical group acts on the -vector space . Then it can induce the actions on the vector space and on the group algebra , respectively. In this paper we determine the structure of -invariant ideals of the group algebra , and establish the relationship between the invariant ideals of and the vector invariant ideals of , if is a unitary group or orthogonal...
Viktoriia Bilet, Oleksiy Dovgoshey, Jürgen Prestin (2015)
Czechoslovak Mathematical Journal
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Let be the set of upper strongly porous at subsets of and let be the intersection of maximal ideals . Some characteristic properties of sets are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at subsets of is a proper subideal of Earlier, completely strongly porous sets and some of their properties...
István Juhász, Lajos Soukup, William Weiss (2006)
Fundamenta Mathematicae
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Let (α) denote the class of all cardinal sequences of length α associated with compact scattered spaces (or equivalently, superatomic Boolean algebras). Also put . We show that f ∈ (α) iff for some natural number n there are infinite cardinals and ordinals such that and where each . Under GCH we prove that if α < ω₂ then (i) ; (ii) if λ > cf(λ) = ω, ; (iii) if cf(λ) = ω₁, ; (iv) if cf(λ) > ω₁, . This yields a complete characterization of the classes (α) for all...
Saharon Shelah, Pauli Väisänen, Jouko Väänänen (2005)
Fundamenta Mathematicae
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Let λ be an infinite cardinal number. The ordinal number δ(λ) is the least ordinal γ such that if ϕ is any sentence of , with a unary predicate D and a binary predicate ≺, and ϕ has a model ℳ with a well-ordering of type ≥ γ, then ϕ has a model ℳ ’ where is non-well-ordered. One of the interesting properties of this number is that the Hanf number of is exactly . It was proved in [BK71] that if ℵ₀ < λ < κ2λ = κ∙ ; ∙ cf(θ) ≥ λ⁺ and whenever μ < θ; ∙ . Then there...
J. Feinstein, D. Somerset (2000)
Studia Mathematica
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Let A be a unital Banach function algebra with character space . For , let and be the ideals of functions vanishing at x and in a neighbourhood of x, respectively. It is shown that the hull of is connected, and that if x does not belong to the Shilov boundary of A then the set has an infinite connected subset. Various related results are given.
Mehrdad Nasernejad, Kazem Khashyarmanesh, Leslie G. Roberts, Jonathan Toledo (2022)
Czechoslovak Mathematical Journal
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Let be an ideal in a commutative Noetherian ring . Then the ideal has the strong persistence property if and only if for all , and has the symbolic strong persistence property if and only if for all , where denotes the th symbolic power of . 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...
Joan Bagaria, Carles Casacuberta, A. R. D. Mathias, Jiří Rosický (2015)
Journal of the European Mathematical Society
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We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopěnka’s principle. We prove that the necessary large-cardinal hypotheses depend on the complexity of the formulas defining the given classes, in the sense of the Lévy hierarchy. For example, the statement that, for a class of morphisms in a locally presentable category of structures, the orthogonal class of objects...
Song-Tao Guo, Hailong Hou, Yong Xu (2015)
Czechoslovak Mathematical Journal
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A graph , with a group of automorphisms of , is said to be -transitive, for some , if is transitive on -arcs but not on -arcs. Let be a connected -transitive graph of prime valency , and the vertex stabilizer of a vertex . Suppose that is solvable. Weiss (1974) proved that . In this paper, we prove that for some positive integers and such that and .
Mehdi Parsinia (2016)
Commentationes Mathematicae Universitatis Carolinae
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Let denote a subalgebra of which is closed under local bounded inversion, briefly, an -subalgebra. These subalgebras were first introduced and studied in Redlin L., Watson S., Structure spaces for rings of continuous functions with applications to realcompactifications, Fund. Math. 152 (1997), 151–163. By characterizing maximal ideals of , we generalize the notion of -ideals, which was first introduced in Acharyya S.K., De D., An interesting class of ideals in subalgebras of ...
Lucia R. Junqueira, Alberto M. E. Levi (2015)
Commentationes Mathematicae Universitatis Carolinae
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We say that a cardinal function reflects an infinite cardinal , if given a topological space with , there exists with . We investigate some problems, discussed by Hodel and Vaughan in Reflection theorems for cardinal functions, Topology Appl. 100 (2000), 47–66, and Juhász in Cardinal functions and reflection, Topology Atlas Preprint no. 445, 2000, related to the reflection for the cardinal functions character and pseudocharacter. Among other results, we present some new equivalences...