A classification scheme for axioms weaker than
G. Ervynck (1991)
Matematički Vesnik
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G. Ervynck (1991)
Matematički Vesnik
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Jeffrey Giansiracusa, Noah Giansiracusa (2022)
Kybernetika
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Given an integral scheme over a non-archimedean valued field , we construct a universal closed embedding of into a -scheme equipped with a model over the field with one element (a generalization of a toric variety). An embedding into such an ambient space determines a tropicalization of by previous work of the authors, and we show that the set-theoretic tropicalization of with respect to this universal embedding is the Berkovich analytification . Moreover, using the scheme-theoretic...
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.
Mei-Chu Chang (2006)
Journal of the European Mathematical Society
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The purpose of this paper is to investigate efficient representations of the residue classes modulo , by performing sum and product set operations starting from a given subset of . We consider the case of very small sets and composite for which not much seemed known (nontrivial results were recently obtained when is prime or when log ). Roughly speaking we show that all residue classes are obtained from a -fold sum of an -fold product set of , where and , provided the...
Hui Wang, Yu Zhang (2023)
Czechoslovak Mathematical Journal
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Let be an integer part of and be the number of positive divisor of . Inspired by some results of M. Jutila (1987), we prove that for , where is the Euler constant and is the Piatetski-Shapiro sequence. This gives an improvement upon the classical result of this problem.
A. Mézard, M. Romagny, D. Tossici (2013)
Annales de l’institut Fourier
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Let be a discrete valuation ring of mixed characteristics , with residue field . Using work of Sekiguchi and Suwa, we construct some finite flat -models of the group scheme of -th roots of unity, which we call . We carefully set out the general framework and algebraic properties of this construction. When is perfect and is a complete totally ramified extension of the ring of Witt vectors , we provide a parallel study of the Breuil-Kisin modules of finite flat models of ,...
Edoardo Ballico (2010)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Let be an integral and non-degenerate -dimensional variety defined over . For any the real -rank is the minimal cardinality of such that . Here we extend to the real case an upper bound for the -rank due to Landsberg and Teitler.
Xiaoqi Wei, Yan Gu (2017)
Czechoslovak Mathematical Journal
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Let (resp. ) be the simplicial complex and the facet ideal (resp. ). When , we give the exact formulas to compute the depth and Stanley depth of quotient rings and for all . When , we compute the depth and Stanley depth of quotient rings and , and give lower bounds for the depth and Stanley depth of quotient rings for all .
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...
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...
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...
Samuel Senti (2003)
Bulletin de la Société Mathématique de France
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For the real quadratic map and a given a point has good expansion properties if any interval containing also contains a neighborhood of with univalent, with bounded distortion and for some . The -weakly expanding set is the set of points which do not have good expansion properties. Let denote the negative fixed point and the first return time of the critical orbit to . We show there is a set of parameters with positive Lebesgue measure for which the Hausdorff...
Erfan Manouchehri, Ali Soleyman Jahan (2021)
Czechoslovak Mathematical Journal
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For each squarefree monomial ideal , we associate a simple finite graph by using the first linear syzygies of . The nodes of are the generators of , and two vertices and are adjacent if there exist variables such that . In the cases, where is a cycle or a tree, we show that has a linear resolution if and only if has linear quotients and if and only if is variable-decomposable. In addition, with the same assumption on , we characterize all squarefree monomial ideals...
Rao Li, Fan Lü, Li Zhou (2024)
Czechoslovak Mathematical Journal
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By iterating the Bolyai-Rényi transformation , almost every real number can be expanded as a continued radical expression with digits for all . For any real number and digit , let be the maximal length of consecutive ’s in the first digits of the Bolyai-Rényi expansion of . We study the asymptotic behavior of the run-length function . We prove that for any digit , the Lebesgue measure of the set is , where . We also obtain that the level set is of full Hausdorff...