Salomon's Theorem for polynomials with several parameters
Schiefkörper über diskret bewerteten Körpern.
Schinzel's problem: Imprimitive covers and the monodromy method
Severi-Brauer varieties of semidirect product algebras.
Shape tiling.
Simples notes, 1° Sur la limite des racines ; 2° Sur un théorème de Cauchy ; 3° Sur une question de licence
Simples remarques sur les racines entières des équations cubiques
Simples remarques sur les racines entières des équations cubiques
Skew fields of noncommutative rational functions (preliminary version)
Small Galois groups that encode valuations
Smith forms of palindromic matrix polynomials.
Solved and unsolved problems οn polynomials
Solving algebraic equations in roots of unity.
Solving Equations, an Elegant Legacy
Solving quadratic equations over polynomial rings of characteristic two.
We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation antn + ...+ a0 = 0 with coefficients ai in A, our problem is to find its roots in A.We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction, we obtain a finite algorithm for solving a polynomial equation over A when A is F[x1, ..., xN] or F(x1,...
Solving the quintic by iteration in three dimensions.
Some Algebraic Properties of Polynomial Rings
In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/ is isomorphic to the field of polynomials with degree smaller than the one of p.
Some classes of irreducible polynomials
Some methods for evaluating the regulator of a real quadratic function field.
Some remarks on a paper by A. McD. Mercer: “Polynomials and convex sequence inequalities” [JIPAM. J. Inequal. Pure Appl. Math. 6, 2005, no. 1, Paper No. 8, 4p., electronic only].