Bounds in the theory of polynomial rings over fields. A nonstandard approach.
Calcul du rayon de la sphère inscrite dans le tétraèdre
Calculs sur les modules projectifs
Central extensions of ordered skew fields.
Characteristic of Rings. Prime Fields
The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over rationals are computed.
Characterizing polynomials by forward differences.
Chebyshev polynomials and Pell equations over finite fields
We shall describe how to construct a fundamental solution for the Pell equation over finite fields of characteristic . Especially, a complete description of the structure of these fundamental solutions will be given using Chebyshev polynomials. Furthermore, we shall describe the structure of the solutions of the general Pell equation .
Combinatorial Nullstellensatz approach to polynomial expansion
Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of |f(A,B)| for finite subsets A, B of a field, and a polynomial f(x,y) of the form f(x,y) = g(x) + yh(x), where the degree of g is greater than that of h.
Commutative Rings and Binomial Coefficients.
Commuting polynomials and self-similarity.
Composite n-forms and Cauchy kernels.
Composite rational functions expressible with few terms
We consider a rational function which is ‘lacunary’ in the sense that it can be expressed as the ratio of two polynomials (not necessarily coprime) having each at most a given number of terms. Then we look at the possible decompositions , where are rational functions of degree larger than 1. We prove that, apart from certain exceptional cases which we completely describe, the degree of is bounded only in terms of (and we provide explicit bounds). This supports and quantifies the intuitive...
Compositum of Galois extensions of hilbertian fields
Conjugated and symmetric polynomial equations. I. Continuous-time systems
Conjugated and symmetric polynomial equations. II. Discrete-time systems
Construction of the mutually orthogonal extraordinary supersquares
Our purpose is to determine the complete set of mutually orthogonal squares of order d, which are not necessary Latin. In this article, we introduce the concept of supersquare of order d, which is defined with the help of its generating subgroup in . We present a method of construction of the mutually orthogonal supersquares. Further, we investigate the orthogonality of extraordinary supersquares, a special family of squares, whose generating subgroups are extraordinary. The extraordinary subgroups...
Corps fini ou champ de Galois
Corrections to "Irreducibility of the iterates of a quadratic polynomial over a field" (Acta Arith. 93 (2000), 87-97)
Corrigendum and addendum to the paper "Reducibility of quadrinomials" (Acta Arith. 21 (1972), 153-171)
Corrigendum: "Galois groups of trinomials" (Acta Arith. 54 (1989), 43-49)