Estimates of
A. Kruse (1967)
Acta Arithmetica
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A. Kruse (1967)
Acta Arithmetica
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Pierre Matet (2013)
Fundamenta Mathematicae
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We discuss the problem of whether there exists a restriction of the noncofinal ideal on that is normal.
Juan Manuel Delgado, Cándido Piñeiro (2015)
Studia Mathematica
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Let be a Banach operator ideal. Based on the notion of -compactness in a Banach space due to Carl and Stephani, we deal with the notion of measure of non–compactness of an operator. We consider a map (respectively, ) acting on the operators of the surjective (respectively, injective) hull of such that (respectively, ) if and only if the operator T is -compact (respectively, injectively -compact). Under certain conditions on the ideal , we prove an equivalence inequality involving...
Keivan Borna, Abolfazl Mohajer (2019)
Czechoslovak Mathematical Journal
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When is a polynomial ring or more generally a standard graded algebra over a field , with homogeneous maximal ideal , it is known that for an ideal of , the regularity of powers of becomes eventually a linear function, i.e., for and some integers , . This motivates writing for every . The sequence , called the of the ideal , is the subject of much research and its nature is still widely unexplored. We know that is eventually constant. In this article, after proving...
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...
Ece Yetkin Çelikel, Hani A. Khashan (2022)
Czechoslovak Mathematical Journal
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Let be a commutative ring with identity. A proper ideal is said to be an -ideal of if for , and imply . We give a new generalization of the concept of -ideals by defining a proper ideal of to be a semi -ideal if whenever is such that , then or . We give some examples of semi -ideal and investigate semi -ideals under various contexts of constructions such as direct products, homomorphic images and localizations. We present various characterizations of this new...
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.
Themba Dube (2017)
Mathematica Bohemica
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Let be a completely regular Hausdorff space and, as usual, let denote the ring of real-valued continuous functions on . The lattice of -ideals of has been shown by Martínez and Zenk (2005) to be a frame. We show that the spectrum of this lattice is (homeomorphic to) precisely when is a -space. This we actually show to be true not only in spaces, but in locales as well. Recall that an ideal of a commutative ring is called a -ideal if whenever two elements have the same annihilator...
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...
S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel (2015)
Commentationes Mathematicae Universitatis Carolinae
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Let be a strong co-ideal of a commutative semiring with identity. Let be a graph with the set of vertices for some , where two distinct vertices and are adjacent if and only if . We look at the diameter and girth of this graph. Also we discuss when is bipartite. Moreover, studies are done on the planarity, clique, and chromatic number of this graph. Examples illustrating the results are presented.
Alain Faisant, Georges Grekos, Ladislav Mišík (2016)
Mathematica Bohemica
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Let be a convergent series of positive real numbers. L. Olivier proved that if the sequence is non-increasing, then . In the present paper: (a) We formulate and prove a necessary and sufficient condition for having ; Olivier’s theorem is a consequence of our Theorem . (b) We prove properties analogous to Olivier’s property when the usual convergence is replaced by the -convergence, that is a convergence according to an ideal of subsets of . Again, Olivier’s theorem is a consequence...
F. Azarpanah, O. A. S. Karamzadeh, S. Rahmati (2008)
Colloquium Mathematicae
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Let be the socle of C(X). It is shown that each prime ideal in is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that , where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points....
Abdelamir Dabbabi, Ali Benhissi (2023)
Archivum Mathematicum
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Let be a commutative ring and a multiplicative system of ideals. We say that is -Noetherian, if for each ideal of , there exist and a finitely generated ideal such that . In this paper, we study the transfer of this property to the polynomial ring and Nagata’s idealization.
Hong Wang, Zhongming Tang (2023)
Czechoslovak Mathematical Journal
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Let be a complete multipartite graph on with and being its binomial edge ideal. It is proved that the Castelnuovo-Mumford regularity is for any positive integer .
Cornelius Greither, Radan Kučera (2014)
Annales de l’institut Fourier
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The aim of this paper is to prove an analog of Gras’ conjecture for an abelian field and an odd prime dividing the degree assuming that the -part of group is cyclic.