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Displaying 301 – 320 of 459

Polynomial Imaginary Decompositions for Finite Separable Extensions

Adam Grygiel (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

Let K be a field and let L = K[ξ] be a finite field extension of K of degree m > 1. If f ∈ L[Z] is a polynomial, then there exist unique polynomials $u ₀, . . ., u_{m - 1} \in K [X ₀, . . ., X_{m - 1}]$ such that $f (\sum_{j = 0}^{m - 1} ξ^{j} X_{j}) = \sum_{j = 0}^{m - 1} ξ^{j} u_{j}$ . A. Nowicki and S. Spodzieja proved that, if K is a field of characteristic zero and f ≠ 0, then $u ₀, . . ., u_{m - 1}$ have no common divisor in $K [X ₀, . . ., X_{m - 1}]$ of positive degree. We extend this result to the case when L is a separable extension of a field K of arbitrary characteristic. We also show that the same is true for a formal power series in several variables....

Polynomial subfields of k (x).

Alan McConnell (1974)

Journal für die reine und angewandte Mathematik

Polynomials of the form $g (x^{k})$ and pseudoprimes with respect to linear recurring sequences

František Marko (1992)

Mathematica Slovaca

Polynomials over $Q$ solving an embedding problem

Nuria Vila (1985)

Annales de l'institut Fourier

The fields defined by the polynomials constructed in E. Nart and the author in J. Number Theory 16, (1983), 6–13, Th. 2.1, with absolute Galois group the alternating group $A_{n}$ , can be embedded in any central extension of $A_{n}$ if and only if $n \equiv 0 (m o d 8)$ , or $n \equiv 2 (m o d 8)$ and $n$ is a sum of two squares. Consequently, for theses values of $n$ , every central extension of $A_{n}$ occurs as a Galois group over $Q$ .

Polynomials whose Galois groups are Frobenius groups with prime order complement

Leonardo Cangelmi (1994)

Journal de théorie des nombres de Bordeaux

We give an effective characterization theorem for integral monic irreducible polynomials $f$ of degree $n$ whose Galois groups over $ℚ$ are Frobenius groups with kernel of order $n$ and complement of prime order.

Polynomials with nontrivial relations between their roots

John D. Dixon (1997)

Acta Arithmetica

Precise study of some number fields and Galois actions occurring in conformal field theory

E. Buffenoir, A. Coste, J. Lascoux, P. Degiovanni, A. Buhot (1995)

Annales de l'I.H.P. Physique théorique

Prehomogeneous vector spaces and field extensions.

David J. Wright, Akihiko Yukie (1992)

Inventiones mathematicae

Primitive elements in rings of holomorphic functions.

Richard M. Hain, T. Duchamp (1984)

Journal für die reine und angewandte Mathematik

Pro-2-Demuskin groups of rank ...0 as Galois groups of maximal 2-extensions of fields.

Roger Ware, Ján Minác (1992)

Mathematische Annalen

Problème de plongement et contraintes galoisiennes sur le groupe des classes

Roland Gillard (1972/1973)

Séminaire de théorie des nombres de Grenoble

Prolongement de la valeur absolue de Gauss et problème de Skolem

Marc Polzin (1988)

Bulletin de la Société Mathématique de France

Pro-p Galois groups of rank ... 4.

Jochen Koenigsmann (1998)

Manuscripta mathematica

Propriété Ci revue et généralisée

Guy Terjanian (1970/1971)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Quadratic forms, division algebras and inseparable multiquadratic extensions. (Formes quadratiques, algèbres à division et extensions multiquadratiques inséparables.)

Mammone, Pasquale, Moresi, Remo (1995)

Bulletin of the Belgian Mathematical Society - Simon Stevin

Quadratic Forms Under Algebraic Extensions.

Richard Elman, T.Y. Lam (1976)

Mathematische Annalen

Quantum-classical interactions and galois type extensions

Władysław Marcinek (2003)

Banach Center Publications

An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is represented by an associative algebra in the category of states. The key new observation is that particle interactions with the quantum environment can be described in terms of Hopf-Galois theory. This opens up a possibility to use quantum groups in our model of particle...

Quartic exercises.

Knus, Max-Albert, Tignol, Jean-Pierre (2003)

International Journal of Mathematics and Mathematical Sciences

Quaternion Extensions of Order 16

Michailov, Ivo (2005)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 12F12We describe several types of Galois extensions having as Galois group the quaternion group Q16 of order 16.This work is partially supported by project of Shumen University.

Quaternion extensions with restricted ramification

Peter Schmid (2014)

Acta Arithmetica

In any normal number field having Q₈, the quaternion group of order 8, as Galois group over the rationals, at least two finite primes must ramify. The classical example by Dedekind of such a field is extraordinary in that it is totally real and only the primes 2 and 3 are ramified. In this note we describe in detail all Q₈-fields over the rationals where only two (finite) primes are ramified. We also show that, for any integer n>3 and any prime $p \equiv 1 (m o d 2^{n - 1})$ , there exist unique real and complex normal number...

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