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 .
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...
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...
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.
Ioana Ghenciu (2015)
Colloquium Mathematicae
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We give sufficient conditions for subsets of compact operators to be weakly precompact. Let (resp. ) denote the set of all w* - w continuous (resp. w* - w continuous compact) operators from E* to F. We prove that if H is a subset of such that H(x*) is relatively weakly compact for each x* ∈ E* and H*(y*) is weakly precompact for each y* ∈ F*, then H is weakly precompact. We also prove the following results: If E has property (wV*) and F has property (V*), then has property (wV*). Suppose...
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.
Daniel Freeman (2008)
Studia Mathematica
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We prove that if is a seminormalized basic sequence and X is a Banach space such that every normalized weakly null sequence in X has a subsequence that is dominated by , then there exists a uniform constant C ≥ 1 such that every normalized weakly null sequence in X has a subsequence that is C-dominated by . This extends a result of Knaust and Odell, who proved this for the cases in which is the standard basis for or c₀.
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...
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...
Ioana Ghenciu (2015)
Commentationes Mathematicae Universitatis Carolinae
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A Banach space has the reciprocal Dunford-Pettis property () if every completely continuous operator from to any Banach space is weakly compact. A Banach space has the (resp. property ) if every -subset of is relatively weakly compact (resp. weakly precompact). We prove that the projective tensor product has property when has the , has property , and .
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...
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...
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 ...
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.
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. ...
Nahid Ashrafi, Marjan Sheibani, Huanyin Chen (2017)
Czechoslovak Mathematical Journal
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A ring is (weakly) nil clean provided that every element in is the sum of a (weak) idempotent and a nilpotent. We characterize nil and weakly nil matrix rings over abelian rings. Let be abelian, and let . We prove that is nil clean if and only if is Boolean and is nil. Furthermore, we prove that is weakly nil clean if and only if is periodic; is , or where is a Boolean ring, and that is weakly nil clean if and only if is nil clean for all .
A. Bouziad, E. Sukhacheva (2017)
Commentationes Mathematicae Universitatis Carolinae
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For a subset of the real line , Hattori space is a topological space whose underlying point set is the reals and whose topology is defined as follows: points from are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on which are sufficient and necessary for to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated...
Ali Akbar Estaji, Maryam Taha (2024)
Czechoslovak Mathematical Journal
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We characterize clean elements of and show that is clean if and only if there exists a clopen sublocale in such that . Also, we prove that is clean if and only if has a clean prime ideal. Then, according to the results about we immediately get results about