Results 11 to 20 of about 3,127 (285)

Parametrization of Algebraic Curves over Optimal Field Extensions

Journal of Symbolic Computation, 1997
In this paper we investigate the problem of determining rational parametrizations of plane algebraic curves over an algebraic extension of least degree over the field of definition.
J Rafael Sendra, Franz Winkler
exaly   +4 more sources

Algebraic extensions of difference fields [PDF]

Transactions of the American Mathematical Society, 1973
An inversive difference field K \mathcal {K} is a field K together with a finite number of automorphisms of K. This paper studies inversive extensions of inversive difference fields whose underlying field extensions are ...
Peter Evanovich
core   +2 more sources

Reverse Mathematics and Algebraic Field Extensions [PDF]

Computability, 2013
This paper analyzes theorems about algebraic field extensions using the techniques of reverse mathematics. In section §2, we show that WKL0 is equivalent to the ability to extend F-automorphisms of field extensions to automorphisms of $\bar F$, the algebraic closure of F. Section §3 explores finitary conditions for embeddability.
François G Dorais, Jeffry L Hirst, Paul Shafer   +2 more
exaly   +3 more sources

Valuations in algebraic field extensions

Journal of Algebra, 2007
Let $K\to L$ be an algebraic field extension and $ν$ a valuation of $K$. The purpose of this paper is to describe the totality of extensions $\left\{ν'\right\}$ of $ν$ to $L$ using a refined version of MacLane's key polynomials. In the basic case when $L$ is a finite separable extension and $rk ν=1$, we give an explicit description of the limit key ...
M A Olalla Acosta, Mark Spivakovsky
exaly   +8 more sources

Solitary Galois Extensions of Algebraic Number Fields

Journal of Number Theory, 1995
A finite extension K of an algebraic number field k is called k-solitary if for any finite extension L of k the equality of norm groups N K/k K* = N L/k L* implies that K and L are conjugate over k (i.e., K and L are k-isomorphic). In the present work we
Guralnick, R.M., Stern, L.
core   +2 more sources

Bicyclic commutator quotients with one non-elementary component [PDF]

Mathematica Bohemica, 2023
For any number field $K$ with non-elementary $3$-class group ${\rm Cl}_3(K)\simeq C_{3^e}\times C_3$, $e\ge2$, the punctured capitulation type $\varkappa(K)$ of $K$ in its unramified cyclic cubic extensions $L_i$, $1\le i\le4$, is an orbit under the ...
Daniel C. Mayer
doaj   +1 more source

Prime Spectrum of the Ring of Adeles of a Number Field

Mathematics, 2022
Much is known about the adele ring of an algebraic number field from the perspective of harmonic analysis and class field theory. However, its ring-theoretical aspects are often ignored.
Álvaro Serrano Holgado
doaj   +1 more source

Algebraic Extensions [PDF]

, 2021
In this article we further develop field theory in Mizar [1], [2], [3] towards splitting fields. We deal with algebraic extensions [4], [5]: a field extension E of a field F is algebraic, if every element of E is algebraic over F. We prove amongst others
Schwarzweller, Christoph, Rowińska-Schwarzweller, Agnieszka   +1 more
core   +1 more source

Finite torsors over strongly $F$-regular singularities [PDF]

Épijournal de Géométrie Algébrique, 2022
We investigate finite torsors over big opens of spectra of strongly $F$-regular germs that do not extend to torsors over the whole spectrum. Let $(R,\mathfrak{m},k)$ be a strongly $F$-regular $k$-germ where $k$ is an algebraically closed field of ...
Javier Carvajal-Rojas
doaj   +1 more source

Projective varieties have countably many real forms

Comptes Rendus. Mathématique, 2023
In this note, we check that a complex projective algebraic variety has (at most) countably many real forms. We more generally prove it when the field of reals is replaced with a field that has only countably many finite extensions up to isomorphism.
Labinet, Timothée L.
doaj   +1 more source