Supremum properties of Galois-type connections

Árpád Száz

Displaying similar documents to “Supremum properties of Galois-type connections”

Random Galois extensions of Hilbertian fields

Lior Bary-Soroker, Arno Fehm (2013)

Journal de Théorie des Nombres de Bordeaux

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Let $L$ be a Galois extension of a countable Hilbertian field $K$ . Although $L$ need not be Hilbertian, we prove that an abundance of large Galois subextensions of $L / K$ are.

Counting discriminants of number fields

Henri Cohen, Francisco Diaz y Diaz, Michel Olivier (2006)

Journal de Théorie des Nombres de Bordeaux

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For each transitive permutation group $G$ on $n$ letters with $n \leq 4$ , we give without proof results, conjectures, and numerical computations on discriminants of number fields $L$ of degree $n$ over $ℚ$ such that the Galois group of the Galois closure of $L$ is isomorphic to $G$ .

On the asymptotics of counting functions for Ahlfors regular sets

Dušan Pokorný, Marc Rauch (2022)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the so-called Ahlfors regular sets (also known as $s$ -regular sets) in metric spaces. First we show that those sets correspond to a certain class of tree-like structures. Building on this observation we then study the following question: Under which conditions does the limit ${lim}_{ε \to 0 +} ε^{s} N (ε, K)$ exist, where $K$ is an $s$ -regular set and $N (ε, K)$ is for instance the $ε$ -packing number of $K$ ?

Universal completely regular dendrites

K. Omiljanowski, S. Zafiridou (2005)

Colloquium Mathematicae

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We define a dendrite $E_{n}$ which is universal in the class of all completely regular dendrites with order of points not greater than n. In particular, the dendrite $E_{ω}$ is universal in the class of all completely regular dendrites. The construction starts with the standard universal dendrite $D_{n}$ of order n described by J. J. Charatonik.

Internally club and approachable for larger structures

John Krueger (2008)

Fundamenta Mathematicae

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We generalize the notion of a fat subset of a regular cardinal κ to a fat subset of $P_{κ} (X)$ , where κ ⊆ X. Suppose μ < κ, $μ^{< μ} = μ$ , and κ is supercompact. Then there is a generic extension in which κ = μ⁺⁺, and for all regular λ ≥ μ⁺⁺, there are stationarily many N in ${[H (λ)]}^{μ ⁺}$ which are internally club but not internally approachable.

The Gibbs phenomenon and Lebesgue constants for regular $A (λ)$ means

V. Swaminathan (1977)

Matematički Vesnik

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Noncommutative numerical motives, Tannakian structures, and motivic Galois groups

Matilde Marcolli, Gonçalo Tabuada (2016)

Journal of the European Mathematical Society

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In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By exploring the change-of-coefficients mechanism, we start by improving some of the main results of [30]. Then, making use of the notion of Schur-finiteness, we prove that the category NNum ${(k)}_{F}$ of noncommutative numerical motives is (neutral) super-Tannakian. As in the commutative world, NNum ${(k)}_{F}$ is not Tannakian. In order to solve this problem we promote periodic cyclic homology to a well-defined...

Arithmetic Properties of Generalized Rikuna Polynomials

Z. Chonoles, J. Cullinan, H. Hausman, A.M. Pacelli, S. Pegado, F. Wei (2014)

Publications mathématiques de Besançon

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Fix an integer $ℓ \geq 3$ . Rikuna introduced a polynomial $r (x, t)$ defined over a function field $K (t)$ whose Galois group is cyclic of order $ℓ$ , where $K$ satisfies some mild hypotheses. In this paper we define the family of ${r_{n} (x, t)}_{n \geq 1}$ of degree $ℓ^{n}$ . The $r_{n} (x, t)$ are constructed iteratively from the $r (x, t)$ . We compute the Galois groups of the $r_{n} (x, t)$ for odd $ℓ$ over an arbitrary base field and give applications to arithmetic dynamical systems.

Regular coordinates and reduction of deformation equations for Fuchsian systems

Yoshishige Haraoka (2012)

Banach Center Publications

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For a Fuchsian system $d Y / d x = (\sum_{j =}^{p} (A_{j}) / (x - t_{j})) Y$ , (F) $t ₁, t ₂, . . ., t_{p}$ being distinct points in ℂ and $A ₁, A ₂, . . ., A_{p} \in M (n \times n; ℂ)$ , the number α of accessory parameters is determined by the spectral types $s (A ₀), s (A ₁), . . ., s (A_{p})$ , where $A ₀ = - \sum_{j = 1}^{p} A_{j}$ . We call the set $z = (z ₁, z ₂, . . ., z_{α})$ of α parameters a regular coordinate if all entries of the $A_{j}$ are rational functions in z. It is not yet known that, for any irreducibly realizable set of spectral types, a regular coordinate does exist. In this paper we study a process of obtaining a new regular coordinate from a given one by a coalescence of eigenvalues...

Preperiodic dynatomic curves for $z \mapsto z^{d} + c$

Yan Gao (2016)

Fundamenta Mathematicae

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The preperiodic dynatomic curve $_{n, p}$ is the closure in ℂ² of the set of (c,z) such that z is a preperiodic point of the polynomial $z \mapsto z^{d} + c$ with preperiod n and period p (n,p ≥ 1). We prove that each $_{n, p}$ has exactly d-1 irreducible components, which are all smooth and have pairwise transverse intersections at the singular points of $_{n, p}$ . We also compute the genus of each component and the Galois group of the defining polynomial of $_{n, p}$ .

Regular elements and Green's relations in Menger algebras of terms

Klaus Denecke, Prakit Jampachon (2006)

Discussiones Mathematicae - General Algebra and Applications

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Defining an (n+1)-ary superposition operation $S^{n}$ on the set $W_{τ} (X_{n})$ of all n-ary terms of type τ, one obtains an algebra $n - c l o n e τ : = (W_{τ} (X_{n}); S^{n}, x_{1}, . . ., x_{n})$ of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation $S^{n}$ there are different possibilities to define binary associative operations on the set $W_{τ} (X_{n})$ and on the cartesian power $W_{τ} {(X_{n})}^{n}$ . In this paper we study idempotent and regular elements as well as Green’s relations in semigroups of terms with these binary associative...