On a decomposition of polynomials in several variables
One considers representation of a polynomial in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.
On a decomposition of polynomials in several variables, II
One considers representation of cubic polynomials in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.
On a polynomial conjecture of Pál Turán
On a problem of Dvornicich and Zannier
On a sequence of nonsolvable quintic polynomials.
On a theorem of Ritt and related Diophantine problems.
On an iterated construction of irreducible polynomials over finite fields of even characteristic by Kyuregyan
We deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by Kyuregyan in 2002, which generalizes the -transform employed previously by Varshamov and Garakov (1969) as well as by Meyn (1990) for the synthesis of irreducible polynomials. While in the iterative procedure described by Kyuregyan the coefficients of the initial polynomial of the sequence have to satisfy certain hypotheses, in the...
On approximate roots of a polynomial.
On canonical subfield preserving polynomials
Explicit monoid structure is provided for the class of canonical subfield preserving polynomials over finite fields. Some classical results and asymptotic estimates will follow as corollaries.
On Commutative Semigroups of Polynomials with Respect to Composition.
On group-permutation polynomials
On Kronecker's elimination theory.
On linear dependence of roots
On mulitplication and factorization of polynomials, II. Irreducibility discussion.
On multiplication and factorization of polynomials, I. Lexicographic orderings and extreme aggregates of terms.
On normal binomials
On ordered division rings
Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel’s axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under for nonzero , instead of requiring that positive elements have a positive product. In this work, this type of ordering is studied in the case of a division ring. It is shown that it actually behaves the same as in the commutative...
On permutation polynomials over finite fields.
On polynomial transformations
On polynomial transformations II