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.
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...
Corrections to "Irreducibility of the iterates of a quadratic polynomial over a field" (Acta Arith. 93 (2000), 87-97)
Corrigendum to "Representatons of multivariate polynomials by sums of univariate polynomials in linear forms" (Colloq. Math. 112 (2008), 201-233)
Corrigendum to the paper: "Linear relations between roots of polynomials" (Acta Arith. 89 (1999), 53-96)
Cycles of polynomials in algebraically closed fields of positive characteristic
Cycles of polynomials in algebraically closed fields of positive characteristic (II)