On m-convex -algebras of type ES
W. Żelazko (1969)
Colloquium Mathematicae
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W. Żelazko (1969)
Colloquium Mathematicae
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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.
Marta Frankowska, Andrzej Nowik (2011)
Colloquium Mathematicae
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We prove that the ideal (a) defined by the density topology is not generated. This answers a question of Z. Grande and E. Strońska.
Vladimir Fonf, Menachem Kojman (2001)
Fundamenta Mathematicae
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We investigate countably convex subsets of Banach spaces. A subset of a linear space is countably convex if it can be represented as a countable union of convex sets. A known sufficient condition for countable convexity of an arbitrary subset of a separable normed space is that it does not contain a semi-clique [9]. A semi-clique in a set S is a subset P ⊆ S so that for every x ∈ P and open neighborhood u of x there exists a finite set X ⊆ P ∩ u such that conv(X) ⊈ S. For closed sets...
Masato Kurihara (1999)
Journal of the European Mathematical Society
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In this paper, for a totally real number field we show the ideal class group of is trivial. We also study the -component of the ideal class group of the cyclotomic -extension.
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....
Pamela Gorkin, Raymond Mortini, Daniel Suárez (2001)
Studia Mathematica
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Let f be a function in the Douglas algebra A and let I be a finitely generated ideal in A. We give an estimate for the distance from f to I that allows us to generalize a result obtained by Bourgain for to arbitrary Douglas algebras.
M. Obradović, S. Owa (1986)
Matematički Vesnik
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James C. Lillo (1967)
Annales Polonici Mathematici
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Piotr Zakrzewski (2015)
Commentationes Mathematicae Universitatis Carolinae
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We give a classical proof of the theorem stating that the -ideal of meager sets is the unique -ideal on a Polish group, generated by closed sets which is invariant under translations and ergodic.
Anna Stasica (2003)
Annales Polonici Mathematici
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We obtain, in a simple way, an estimate for the Noether exponent of an ideal I without embedded components (i.e. we estimate the smallest number μ such that ).
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 < ∞.
Z. Krzeszowiak (1969)
Annales Polonici Mathematici
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H. Fejzić, R. E. Svetic, C. E. Weil (2010)
Fundamenta Mathematicae
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The main result of this paper is that if f is n-convex on a measurable subset E of ℝ, then f is n-2 times differentiable, n-2 times Peano differentiable and the corresponding derivatives are equal, and except on a countable set. Moreover is approximately differentiable with approximate derivative equal to the nth approximate Peano derivative of f almost everywhere.
Stefan Müller, Vladimír Šverák (1999)
Journal of the European Mathematical Society
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We study solutions of first order partial differential relations , where is a Lipschitz map and is a bounded set in matrices, and extend Gromov’s theory of convex integration in two ways. First, we allow for additional constraints on the minors of and second we replace Gromov’s −convex hull by the (functional) rank-one convex hull. The latter can be much larger than the former and this has important consequences for the existence of ‘wild’ solutions to elliptic systems. Our...
Antoni Wawrzyńczyk (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let B be a complex topological unital algebra. The left joint spectrum of a set S ⊂ B is defined by the formula = generates a proper left idealUsing the Schur lemma and the Gelfand-Mazur theorem we prove that has the spectral mapping property for sets S of pairwise commuting elements if (i) B is an m-convex algebra with all maximal left ideals closed, or (ii) B is a locally convex Waelbroeck algebra. The right ideal version of this result is also valid.
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.
Marek Pycia
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This paper solves the functional inequality af(s) + bf(t) ≥ f(αs + βt), s,t > 0, with four positive parameters a,b,α,β arbitrarily fixed. The unknown function f: (0,∞) → ℝ is assumed to satisfy the regularity condition . The paper partitions the space of parameters into regions where the inequality has qualitatively similar classes of solutions, estimates the rate of growth of the solutions, determines their signs, and identifies all the parameters such that the solutions form small...
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...
Z. Kominek (1974)
Annales Polonici Mathematici
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C. T. Ng (1973)
Annales Polonici Mathematici
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J. Cabello, E. Nieto (1998)
Studia Mathematica
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C.-M. Cho and W. B. Johnson showed that if a subspace E of , 1 < p < ∞, has the compact approximation property, then K(E) is an M-ideal in ℒ(E). We prove that for every r,s ∈ ]0,1] with , the James space can be provided with an equivalent norm such that an arbitrary subspace E has the metric compact approximation property iff there is a norm one projection P on ℒ(E)* with Ker P = K(E)⊥ satisfying ∥⨍∥ ≥ r∥Pf∥ + s∥φ - Pf∥ ∀⨍ ∈ ℒ(E)*. A similar result is proved for subspaces of...
M. Malenica (1982)
Matematički Vesnik
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