The factorization of over a finite field where is of first degree and L(x) is linear
The Fekete-Szegő theorem with splitting conditions: Part II
The field of Nash functions and factorization of polynomials
The algebraically closed field of Nash functions is introduced. It is shown that this field is an algebraic closure of the field of rational functions in several variables. We give conditions for the irreducibility of polynomials with Nash coefficients, a description of factors of a polynomial over the field of Nash functions and a theorem on continuity of factors.
The Field of Reals with a Predicate for the Powers of Two.
The five-variable Volterra system
We give a description of all polynomial constants of the five-variable Volterra derivation, hence of all polynomial first integrals of its corresponding Volterra system of differential equations. The Volterra system plays a significant role in plasma physics and population biology.
The formal inverse and the Jacobian Conjecture
The fourteenth problem of Hilbert for polynomial derivations
We present some facts, observations and remarks concerning the problem of finiteness of the rings of constants for derivations of polynomial rings over a commutative ring k containing the field ℚ of rational numbers.
The fundamental group of a Galois cover of .
The Galois Cohomology of Pythagorean Fields.
The Galois Group of a Radical Extension of the Rationals.
The Galois group of generic symmetric matrices
The Galois relation x₁ = x₂ + x₃ for finite simple groups
The Galois relation x₁ = x₂+x₃ and Fermat over finite fields
The geometry of the set of characters iduced by valuations.
The Global Homological Dimension of Some Algebras of Differential Operators.
The group of automorphisms of algebraic function fields.
The Hasse conjecture for cyclic extensions.
The Hasse principle for homogeneous spaces.
The Hilbert Modular Surface of a Real Quadratic Field.
The identity of three classes of polynomials.