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 .
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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 .
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...
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...
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.
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. ...
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.
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...
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...
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...
Cheng Gong, Zhongming Tang (2015)
Czechoslovak Mathematical Journal
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Let be a monomial ideal and the multiplier ideal of with coefficient . Then is also a monomial ideal of , and the equality implies that . We mainly discuss the problem when or for all . It is proved that if then is principal, and if holds for all then . One global result is also obtained. Let be the ideal sheaf on associated with . Then it is proved that the equality implies that is principal.
Thomas Vils Pedersen (2004)
Studia Mathematica
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For 0 < γ ≤ 1, let be the big Lipschitz algebra of functions analytic on the open unit disc which satisfy a Lipschitz condition of order γ on ̅. For a closed set E on the unit circle and an inner function Q, let be the closed ideal in consisting of those functions for which (i) f = 0 on E, (ii) as d(z,E),d(w,E) → 0, (iii) . Also, for a closed ideal I in , let = z ∈ : f(z) = 0 for every f ∈ I and let be the greatest common divisor of the inner parts of non-zero functions...
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.
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.
Vittoria Bonanzinga, Loredana Sorrenti (2008)
Bollettino dell'Unione Matematica Italiana
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In this paper we determine all squarefree completely lexsegment ideals which have a linear resolution. Let denote the set of all squarefree monomials of degree in a polynomial ring in variables over a field . We order the monomials lexicographically such that , thus a lexsegment (of degree ) is a subset of of the form for some con . An ideal generated by a lexsegment is called a lexsegment ideal. We describe the procedure to determine when such an ideal has a linear...
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 ...
Manuel González, José M. Herrera (2007)
Studia Mathematica
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We consider real Banach spaces X for which the quotient algebra (X)/ℐn(X) is finite-dimensional, where ℐn(X) stands for the ideal of inessential operators on X. We show that these spaces admit a decomposition as a finite direct sum of indecomposable subspaces for which is isomorphic as a real algebra to either the real numbers ℝ, the complex numbers ℂ, or the quaternion numbers ℍ. Moreover, the set of subspaces can be divided into subsets in such a way that if and are in different...
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...