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...
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...
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...
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....
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.
Chia-chi Tung (2013)
Annales Polonici Mathematici
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Conditions characterizing the membership of the ideal of a subvariety arising from (effective) divisors in a product complex space Y × X are given. For the algebra of relative regular functions on an algebraic variety V, the strict stability is proved, in the case where Y is a normal space, and the Noether stability is established under a weakened condition. As a consequence (for both general and complete intersections) a global Nullstellensatz is derived for divisors in , respectively,...
Hai Mau Le, Hong Xuan Nguyen, Hung Viet Vu (2015)
Annales Polonici Mathematici
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We give some characterizations of the class and use them to establish a lower estimate for the log canonical threshold of plurisubharmonic functions in this class.
Dongyang Chen, William B. Johnson, Bentuo Zheng (2014)
Studia Mathematica
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We give a corrected proof of Theorem 2.10 in our paper “Commutators on ” [Studia Math. 206 (2011), 175-190] for the case 1 < q < p < ∞. The case when 1 = q < p < ∞ remains open. As a consequence, the Main Theorem and Corollary 2.17 in that paper are only valid for 1 < p,q < ∞.
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...
Zbigniew Lipecki (2017)
Commentationes Mathematicae Universitatis Carolinae
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Let and be algebras of subsets of a set with , and denote by the set of all quasi-measure extensions of a given quasi-measure on to . We show that is order bounded if and only if it is contained in a principal ideal in if and only if it is weakly compact and is contained in a principal ideal in . We also establish some criteria for the coincidence of the ideals, in , generated by and .
D. W. Hajek, I. Irizarry (1981)
Matematički Vesnik
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A. Pełczyński, H. Rosenthal (1975)
Studia Mathematica
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Swami Jnanananda (1936)
Časopis pro pěstování matematiky a fysiky
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Krzysztof Kołodziejczyk (1987)
Colloquium Mathematicae
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Th. Friedrich (1974)
Colloquium Mathematicae
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