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 .
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...
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.
Stefania Gabelli (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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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.
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.
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...
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.
Khalid A. Mokbel (2015)
Mathematica Bohemica
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The concept of -ideals in posets is introduced. Several properties of -ideals in -distributive posets are studied. Characterization of prime ideals to be -ideals in -distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal of a -distributive poset is non-dense, then is an -ideal. Moreover, it is shown that the set of all -ideals of a poset with forms a complete lattice. A result analogous to separation theorem for...
Matthew Daws, Volker Runde (2008)
Studia Mathematica
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It is known that is not amenable for p = 1,2,∞, but whether or not is amenable for p ∈ (1,∞) ∖ 2 is an open problem. We show that, if is amenable for p ∈ (1,∞), then so are and . Moreover, if is amenable so is for any index set and for any infinite-dimensional -space E; in particular, if is amenable for p ∈ (1,∞), then so is . We show that is not amenable for p = 1,∞, but also that our methods fail us if p ∈ (1,∞). Finally, for p ∈ (1,2) and a free ultrafilter over...
Khalid A. Mokbel (2016)
Mathematica Bohemica
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The concept of a -ideal in -distributive posets is introduced. Several properties of -ideals in -distributive posets are established. Further, the interrelationships between -ideals and -ideals in -distributive posets are investigated. Moreover, a characterization of prime ideals to be -ideals in -distributive posets is obtained in terms of non-dense ideals. It is shown that every -ideal of a -distributive meet semilattice is semiprime. Several counterexamples are discussed. ...
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...
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 ...
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.
Dumitru Popa (2013)
Studia Mathematica
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Let 1 ≤ p < ∞, be a sequence of Banach spaces and the coresponding vector valued sequence space. Let , be two sequences of Banach spaces, , Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator by . We give necessary and sufficient conditions for to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞. ...
M. J. Nikmehr, B. Soleymanzadeh (2017)
Commentationes Mathematicae Universitatis Carolinae
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Let be a commutative ring with unity and be the set of unit elements of . In this paper, we introduce and investigate some properties of a new kind of graph on the ring , namely, the prime ideals intersection graph of , denoted by . The is a graph with vertex set and two distinct vertices and are adjacent if and only if there exists a prime ideal of such that . We obtain necessary and sufficient conditions on such that is disconnected. We find the diameter and...
Ali Yassine, Mohammad Javad Nikmehr, Reza Nikandish (2024)
Czechoslovak Mathematical Journal
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Let be a commutative ring with identity. We study the concept of strongly 1-absorbing primary ideals which is a generalization of -ideals and a subclass of -absorbing primary ideals. A proper ideal of is called strongly 1-absorbing primary if for all nonunit elements such that , it is either or . Some properties of strongly 1-absorbing primary ideals are studied. Finally, rings over which every semi-primary ideal is strongly 1-absorbing primary, and rings over which...
Jan Kraszewski (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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We compute transitive cardinal coefficients of ideals on generalized Cantor spaces. In particular, we show that there exists a null set such that for every null set we can find such that A ∪ (A+x) cannot be covered by any translation of B.
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...
Stephan Baier (2005)
Acta Arithmetica
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David Grow (1987)
Colloquium Mathematicae
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M. K. Sen (1971)
Annales Polonici Mathematici
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Kristóf Szarvas, Ferenc Weisz (2016)
Czechoslovak Mathematical Journal
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The classical Hardy-Littlewood maximal operator is bounded not only on the classical Lebesgue spaces (in the case ), but (in the case when is log-Hölder continuous and ) on the variable Lebesgue spaces , too. Furthermore, the classical Hardy-Littlewood maximal operator is of weak-type . In the present note we generalize Besicovitch’s covering theorem for the so-called -rectangles. We introduce a general maximal operator and with the help of generalized -functions, the strong-...